Greek letters used in mathematics, science, and engineering

Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities. Those Greek letters which have the same form as Latin letters are rarely used: capital A, B, E, Z, H, I, K, M, N, O, P, T, Y, X. Small ι, ο and υ are also rarely used, since they closely resemble the Latin letters i, o and u. Sometimes, font variants of Greek letters are used as distinct symbols in mathematics, in particular for ε/ϵ and π/ϖ. The archaic letter digamma (Ϝ/ϝ/ϛ) is sometimes used.

The Bayer designation naming scheme for stars typically uses the first Greek letter, α, for the brightest star in each constellation, and runs through the alphabet before switching to Latin letters.

In mathematical finance, the Greeks are the variables denoted by Greek letters used to describe the risk of certain investments.

Typography

Some common conventions:

• Intensive quantities in physics are usually denoted with minuscules
  while extensive are denoted with capital letters.
• Most symbols are written in italics.
• Vectors can be denoted in boldface.
• Sets of numbers are typically bold or blackboard bold.

The Greek letter forms used in mathematics are often different from those used in Greek-language text: they are designed to be used in isolation, not connected to other letters, and some use variant forms which are not normally used in current Greek typography.

The OpenType font format has the feature tag "mgrk" ("Mathematical Greek") to identify a glyph as representing a Greek letter to be used in mathematical (as opposed to Greek language) contexts.

The table below shows a comparison of Greek letters rendered in TeX and HTML. The font used in the TeX rendering is an italic style. This is in line with the convention that variables should be italicized. As Greek letters are more often than not used as variables in mathematical formulas, a Greek letter appearing similar to the TeX rendering is more likely to be encountered in works involving mathematics.

Greek letters in HTML and TeX (α–μ)

Name	TeX	HTML
Alpha	${\displaystyle \mathrm {A} \,\alpha }$	Α α
Beta	${\displaystyle \mathrm {B} \,\beta }$	Β β
Gamma	${\displaystyle \Gamma \,\gamma }$	Γ γ
Delta	${\displaystyle \Delta \,\delta }$	Δ δ
Epsilon	${\displaystyle \mathrm {E} \,\epsilon \,\varepsilon }$	Ε ϵ ε
Digamma	${\displaystyle \mathrm {\Digamma} \,\digamma }$	Ϝ ϝ
Zeta	${\displaystyle \mathrm {Z} \,\zeta }$	Ζ ζ
Eta	${\displaystyle \mathrm {H} \,\eta }$	Η η
Theta	${\displaystyle \Theta \,\theta \,\vartheta }$	Θ θ ϑ
Iota	${\displaystyle \mathrm {I} \,\iota }$	Ι ι
Kappa	${\displaystyle \mathrm {K} \,\kappa \,\varkappa }$	Κ κ ϰ
Lambda	${\displaystyle \Lambda \,\lambda }$	Λ λ
Mu	${\displaystyle \mathrm {M} \,\mu }$	Μ μ

Greek letters in HTML and TeX (ν–ω)

Name	TeX	HTML
Nu	${\displaystyle \mathrm {N} \,\nu }$	Ν ν
Xi	${\displaystyle \Xi \,\xi }$	Ξ ξ
Omicron	${\displaystyle \mathrm {O} \,o}$	Ο ο
Pi	${\displaystyle \Pi \,\pi \,\varpi }$	Π π ϖ
Rho	${\displaystyle \mathrm {P} \,\rho \,\varrho }$	Ρ ρ ϱ
Sigma	${\displaystyle \Sigma \,\sigma \,\varsigma }$	Σ σ ς
Tau	${\displaystyle \mathrm {T} \,\tau }$	Τ τ
Upsilon	${\displaystyle \Upsilon \,\upsilon }$	Υ υ
Phi	${\displaystyle \Phi \,\phi \,\varphi }$	Φ ϕ φ
Chi	${\displaystyle \mathrm {X} \,\chi }$	Χ χ
Psi	${\displaystyle \Psi \,\psi }$	Ψ ψ
Omega	${\displaystyle \Omega \,\omega }$	Ω ω

Greek letters with typographical variations

Name	Greek Letter	Bold	Italic	Bold Italic	Sans-Serif Bold	Sans-Serif Bold Italic	APL	Double struck bold	Unicode variants or similar
Alpha	Α α	𝚨 𝛂	𝛢 𝛼	𝜜 𝜶	𝝖 𝝰	𝞐 𝞪	⍺ ⍶
Beta	Β β ϐ ᵝ ᵦ	𝚩 𝛃	𝛣 𝛽	𝜝 𝜷	𝝗 𝝱	𝞑 𝞫
Gamma	Γ γ ᴦ ᵞ ᵧ	𝚪 𝛄	𝛤 𝛾	𝜞 𝜸	𝝘 𝝲	𝞒 𝞬		ℾ ℽ
Delta	Δ δ ᵟ	𝚫 𝛅	𝛥 𝛿	𝜟 𝜹	𝝙 𝝳	𝞓 𝞭			U+2206∆INCREMENT, U+2207∇NABLA
Epsilon	Ε ε ϵ ϶	𝚬 𝛆 𝛜	𝛦 𝜀 𝜖	𝜠 𝜺 𝝐	𝝚 𝝴 𝞊	𝞔 𝞮 𝟄	⍷		U+2208∈ELEMENT OF–U+220D∍SMALL CONTAINS AS MEMBER
Zeta	Ζ ζ	𝚭 𝛇	𝛧 𝜁	𝜡 𝜻	𝝛 𝝵	𝞕 𝞯
Eta	Η η Ͱ ͱ	𝚮 𝛈	𝛨 𝜂	𝜢 𝜼	𝝜 𝝶	𝞖 𝞰
Theta	Θ θ ϑ ϴ ᶿ	𝚯 𝛉 𝚹 𝛝	𝛩 𝜃 𝛳 𝜗	𝜣 𝜽 𝜭 𝝑	𝝝 𝝷 𝚹 𝞋	𝞗 𝞱 𝜭 𝟅
Iota	Ι ι ᶥ ℩	𝚰 𝛊	𝛪 𝜄	𝜤 𝜾	𝝞 𝝸	𝞘 𝞲	⍳ ⍸
Kappa	Κ κ ϰ	𝚱 𝛋 𝛞	𝛫 𝜅 𝜘	𝜥 𝜿 𝝒	𝝟 𝝹 𝞌	𝞙 𝞳 𝟆
Lambda	Λ λ ᴧ	𝚲 𝛌	𝛬 𝜆	𝜦 𝝀	𝝠 𝝺	𝞚 𝞴
Mu	Μ μ	𝚳 𝛍	𝛭 𝜇	𝜧 𝝁	𝝡 𝝻	𝞛 𝞵
Nu	Ν ν	𝚴 𝛎	𝛮 𝜈	𝜨 𝝂	𝝢 𝝼	𝞜 𝞶
Xi	Ξ ξ	𝚵 𝛏	𝛯 𝜉	𝜩 𝝃	𝝣 𝝽	𝞝 𝞷
Omicron	Ο ο	𝚶 𝛐	𝛰 𝜊	𝜪 𝝄	𝝤 𝝾	𝞞 𝞸
Pi	Π π ϖ ᴨ	𝚷 𝛑 𝛡	𝛱 𝜋 𝜛	𝜫 𝝅 𝝕	𝝥 𝝿 𝞏	𝞟 𝞹 𝟉		ℿ ℼ	U+220F∏N-ARY PRODUCT, U+2210∐N-ARY COPRODUCT
Rho	Ρ ρ Ῥ ῥ ῤ ϱ ϼ ᴩ ᵨ ☧	𝚸 𝛒 𝛠	𝛲 𝜌 𝜚	𝜬 𝝆 𝝔	𝝦 𝞀 𝞎	𝞠 𝞺 𝟈	⍴
Sigma	Σ σ ς Ϲ ϲ Ͻ ͻ Ͼ ͼ Ͽ ͽ	𝚺 𝛔 𝛓	𝛴 𝜎 𝜍	𝜮 𝝈 𝝇	𝝨 𝞂 𝞁	𝞢 𝞼 𝞻		⅀	U+2211∑N-ARY SUMMATION
Tau	Τ τ	𝚻 𝛕	𝛵 𝜏	𝜯 𝝉	𝝩 𝞃	𝞣 𝞽
Upsilon	Υ υ ϒ	𝚼 𝛖	𝛶 𝜐	𝜰 𝝊	𝝪 𝞄	𝞤 𝞾
Phi	Φ φ ϕ	𝚽 𝛗 𝛟	𝛷 𝜑 𝜙	𝜱 𝝋 𝝓	𝝫 𝞅 𝞍	𝞥 𝞿 𝟇
Chi	Χ χᵡᵪ☧	𝚾 𝛘	𝛸 𝜒	𝜲 𝝌	𝝬 𝞆	𝞦 𝟀
Psi	Ψ ψ ᴪ	𝚿 𝛙	𝛹 𝜓	𝜳 𝝍	𝝭 𝞇	𝞧 𝟁
Omega	Ω ω ꭥ	𝛀 𝛚	𝛺 𝜔	𝜴 𝝎	𝝮 𝞈	𝞨 𝟂	⍵ ⍹		U+2126ΩOHM SIGN, U+2127℧INVERTED OHM SIGN

Concepts represented by a Greek letter

Αα (alpha)

See also: Alpha (disambiguation)

• ${\displaystyle \alpha }$ represents:
  • the first angle in a triangle, opposite the side a
  • the statistical significance of a result
  • the false positive rate in statistics ("Type I" error) ^[1]
  • the fine-structure constant in physics ^{[2] [3]}
  • the angle of attack of an aircraft
  • an alpha particle (He²⁺)
  • angular acceleration in physics ^[4]
  • the linear thermal expansion coefficient
  • the thermal diffusivity ^[5]
  • In organic chemistry the α-carbon is the backbone carbon next to the carbonyl carbon, most often for amino acids
  • right ascension in astronomy ^[6]
  • the brightest star in a constellation ^[7]
  • Iron ferrite and numerous phases within materials science
  • the return in excess of the compensation for the risk borne in investment
  • the α-conversion in lambda calculus
  • the independence number of a graph
  • a placeholder for ordinal numbers in mathematical logic
  •  a type of receptor for the neurotransmitter noradrenaline in neuroscience

Ββ (beta)

See also: Beta (disambiguation)

• ${\displaystyle \mathrm {B} }$ represents the beta function
• ${\displaystyle \beta }$ represents:
  • the thermodynamic beta, equal to (k_BT)⁻¹, where k_B is the Boltzmann constant and T is the absolute temperature.
  • the second angle in a triangle, opposite the side b
  • the standardized regression coefficient for predictor or independent variables in linear regression (unstandardized regression coefficients are represented with the lower-case Latin b, but are often called "betas" as well)
  • the ratio of collector current to base current in a bipolar junction transistor (BJT) in electronics (current gain)
  • the false negative rate in statistics ("Type II" error) ^[8]
  • the beta coefficient, the non-diversifiable risk, of an asset in mathematical finance
  • the sideslip angle of an airplane
  • a beta particle (e⁻ or e⁺)
  • the beta brain wave in brain or cognitive sciences ^[9]
  • ecliptic latitude in astronomy ^[10]
  • the ratio of plasma pressure to magnetic pressure in plasma physics ^[11]
  • β-reduction in lambda calculus
  • the ratio of the velocity of an object to the speed of light as used in the Lorentz factor ^[12]
  • a type of receptor for the noradrenaline neurotransmitter in neuroscience

Γγ (gamma)

See also: Gamma (disambiguation)

• ${\displaystyle \Gamma }$ represents:
  • the circulation in fluid dynamics
  • the reflection coefficient of a transmission or telecommunication line. ^[13]
  • the confinement factor of an optical mode in a waveguide
  • the gamma function, a generalization of the factorial ^[14]
  • the upper incomplete gamma function
  • the modular group, the group of fractional linear transformations
  • the gamma distribution, a continuous probability distribution defined using the gamma function ^[15]
  • second-order sensitivity to price in mathematical finance
  • the Christoffel symbols that describe components of a metric connection ^[16]
  • the stack alphabet in the formal definition of a pushdown automaton, or the tape-alphabet in the formal definition of a Turing machine
  • the Feferman–Schütte ordinal Γ₀ ^[17]
• ${\displaystyle \gamma }$ represents:
  • the specific weight of substances
  • the lower incomplete gamma function
  • the third angle in a triangle, opposite the side c
  • the Euler–Mascheroni constant in mathematics ^[18]
  • gamma rays and the photon
  • the heat capacity ratio in thermodynamics
  • the Lorentz factor in special relativity ^[19]
  • the flight path angle of an airplane

Δδ (delta)

See also: Delta (disambiguation)

• ${\displaystyle \Delta }$ represents:
  • a finite difference
  • a difference operator
  • a symmetric difference
  • the Laplace operator
  • giving heat in a chemical reaction
  • the angle that subtends the arc of a circular curve in surveying
  • the maximum degree of any vertex in a given graph
  • sensitivity to price in mathematical finance
  • the discriminant of a polynomial (in a quadratic polynomial determines the nature of the roots)
• ${\displaystyle \delta }$ represents:
  • percent error
  • a variation in the calculus of variations
  • the Kronecker delta function ^[20]
  • the Feigenbaum constants ^[21]
  • the force of interest in mathematical finance
  • the Dirac delta function ^[22]
  • the receptor which enkephalins have the highest affinity for in pharmacology ^[23]
  • the Skorokhod integral in Malliavin calculus, a subfield of stochastic analysis
  • the minimum degree of any vertex in a given graph
  • a partial charge. δ− represents a negative partial charge, and δ+ represents a positive partial charge chemistry (See also: Solvation)
  • the chemical shift of an atomic nucleus in NMR spectroscopy. For protons, this is relative to tetramethylsilane = 0
  • stable isotope compositions
  • declination in astronomy ^[24]
  • noncentrality measure in statistics ^[25]
  • The transition function in the formal definition of a finite automaton, pushdown automaton, or Turing machine
  • Infinitesimal - see Limit of a function § (ε, δ)-definition of limit
• Not to be confused with ∂ which is based on the Latin letter d but often called a "script delta"

Εε (epsilon)

See also: Epsilon (disambiguation)

• ${\displaystyle \epsilon }$ represents:
  • a small positive quantity; see limit
  • a random error in regression analysis
  • the absolute value of an error ^[26]
  • in set theory, the limit ordinal of the sequence ${\displaystyle \omega ,\omega ^{\omega },\omega ^{\omega ^{\omega }},\dots }$
  • in computer science, the empty string
  • the Levi-Civita symbol
  • in electromagnetics, dielectric permittivity ^[27]
  • emissivity
  • strain in continuum mechanics
  • permittivity ^[28]
  • the Earth's axial tilt in astronomy ^[29]
  • elasticity in economics ^[30]
  • electromotive force
  • in chemistry, the molar extinction coefficient of a chromophore
  • in mathematics, a surreal number that is bigger than zero, but smaller than all positive real numbers.
• set membership symbol ∈ is based on ε

Ϝϝ (digamma)

See also: Digamma

• Ϝ is sometimes used to represent the digamma function, though the Latin letter F (which is nearly identical) is usually substituted.
• A hypothetical particle Ϝ speculated to be implicated in the 750 GeV diphoton excess, now known to be simply a statistical anomaly

Ζζ (zeta)

See also: Zeta (disambiguation)

• ${\displaystyle \zeta }$ represents:
  • the Riemann zeta function and other zeta functions in mathematics
  • the damping ratio ^[31]
  • the value for the Zeta potential, i.e., the electrical potential at the slipping plane, used often in colloidal chemistry ^[32]

Ηη (eta)

See also: Eta (disambiguation)

• ${\displaystyle \mathrm {H} }$ represents:
  • the Eta function of Ludwig Boltzmann's H-theorem ("Eta" theorem), in statistical mechanics
  • Information theoretic (Shannon) entropy
• ${\displaystyle \eta }$ represents:
  • the intrinsic wave impedance of a medium (e.g. the impedance of free space)
  • the partial regression coefficient in statistics, also interpreted as an effect size measure for analyses of variance
  • the eta meson
  • viscosity ^[33]
  • the Dedekind eta function ^[34]
  • energy conversion efficiency ^[35]
  • efficiency (physics)
  • the Minkowski metric tensor in relativity ^[36]
  • η-conversion in lambda calculus ^[37]
  • the learning rate in machine learning and statistics ^[38]

Θθ (theta)

See also: Theta (disambiguation)

• ${\displaystyle \Theta }$ (uppercase) represents:
  • an asymptotically tight bound related to big O notation.
  • sensitivity to the passage of time in mathematical finance
  • in set theory, a certain ordinal number
  • Heaviside step function
• ${\displaystyle \theta }$ (lowercase) represents:
  • a plane angle in geometry
  • the angle to the x axis in the xy-plane in spherical or cylindrical coordinates (mathematics)
  • the angle to the z axis in spherical coordinates (physics)
  • the potential temperature in thermodynamics
  • theta functions
  • the angle of a scattered photon during a Compton scattering interaction
  • the angular displacement of a particle rotating about an axis
  • the Watterson estimator in population genetics
  • the thermal resistance between two bodies
• ϑ ("script theta"), the cursive form of theta, often used in handwriting, represents
  • the first Chebyshev function in number theory
  • Theta role in linguistics

Ιι (iota)

See also: Iota (disambiguation)

• ${\displaystyle \iota }$ represents:
  • an inclusion map in set theory
  • the index generator function in APL (in the form ⍳)
  • the interior product

Κκ (kappa)

See also: Kappa (disambiguation)

• ${\displaystyle \mathrm {K} }$ represents:
  • the Kappa number, indicating lignin content in pulp
• ${\displaystyle \kappa }$ represents:
  • the Von Kármán constant, describing the velocity profile of turbulent flow
  • the kappa curve, a two-dimensional algebraic curve ^[39]
  • the condition number of a matrix in numerical analysis
  • the connectivity of a graph in graph theory ^[40]
  • curvature ^[41]
  • dielectric constant ${\displaystyle (\varepsilon /\varepsilon _{0})}$
  • thermal conductivity (usually a lowercase Latin ${\displaystyle k}$) ^[42]
  • electrical conductivity of a solution ^[43]
  • thermal diffusivity
  • a spring constant (usually a lowercase Latin ${\displaystyle k}$)
  • the heat capacity ratio in thermodynamics (usually ${\displaystyle \gamma }$)
  • the receptor which dynorphins have the highest affinity for in pharmacology ^[23]
  • Einstein gravitational constant ^[44]

Λλ (lambda)

See also: Lambda (disambiguation)

• ${\displaystyle \Lambda }$ represents:
  • the Lebesgue constant, a bound for the interpolation error
  • the von Mangoldt function in number theory
  • the set of logical axioms in the axiomatic method of logical deduction in first-order logic
  • the cosmological constant
  • the lambda baryon
  • a diagonal matrix of eigenvalues in linear algebra
  • a lattice
  • molar conductivity in electrochemistry
  • Iwasawa algebra
• ${\displaystyle \lambda }$ represents:
  • one wavelength of electromagnetic radiation
  • the decay constant in radioactivity ^[45]
  • function expressions in the lambda calculus
  • a general eigenvalue in linear algebra
  • the expected number of occurrences in a Poisson distribution in probability
  • the arrival rate in queueing theory
  • the failure rate in reliability engineering
  • the Lagrange multiplier in mathematical optimization, known as the shadow price in economics
  • the Lebesgue measure denotes the volume or measure of a Lebesgue measurable set
  • longitude in geodesy
  • linear density
  • ecliptic longitude in astronomy ^[46]
  • the Liouville function in number theory
  • the Carmichael function in number theory
  • the empty string in formal grammar
  • a formal system (lambda calculus) in mathematical logic
  • thermal conductivity
  • the Lorentz transformation

Μμ (mu)

See also: Mu (disambiguation)

• ${\displaystyle \mu }$ represents:
  • the Möbius function in number theory
  • the population mean or expected value in probability and statistics
  • a measure in measure theory
  • micro-, an SI prefix denoting 10⁻⁶ (one millionth)
  • Micrometre or micron (retired in 1967 as a standalone symbol, replaced by "μm" using the standard SI meaning)
  • the coefficient of friction in physics
  • the service rate in queueing theory
  • the dynamic viscosity in physics
  • magnetic permeability in electromagnetics ^[47]
  • a muon ^[48]
  • reduced mass ^[49]
  • the ion mobility in plasma physics
  • the Standard gravitational parameter in celestial mechanics
  • population mean in statistics
  • chemical potential in thermodynamics
  • Absorption coefficient
  • Amplification factor
  • Magnetic moment of a dipole ^[50]

Νν (nu)

See also: Nu (disambiguation)

• ${\displaystyle \nu }$ represents:
  • frequency in physics in hertz (Hz)
  • Poisson's ratio in materials science
  • a neutrino ^[51]
  • kinematic viscosity of liquids ^[52]
  • stoichiometric coefficient in chemistry
  • true anomaly in celestial mechanics ^[53]
  • degrees of freedom in statistics
  • the matching number of a graph
  • the p-adic valuation of a number

Ξξ (xi)

See also: Xi (disambiguation)

• ${\displaystyle \Xi }$ represents:
  • the original Riemann Xi function, i.e. Riemann's lower case ξ, as denoted by Edmund Landau and currently
  • the xi baryon
• ${\displaystyle \xi }$ represents:
  • the original Riemann Xi function
  • the modified definition of Riemann xi function, as denoted by Edmund Landau
  • the extent of reaction

Οο (omicron)

See also: Omicron (disambiguation)

Ππ (pi)

See also: Pi (disambiguation)

• ${\displaystyle \Pi }$ represents:
  • the product operator in mathematics
  • a plane
  • the unary projection operation in relational algebra
  • the Pi function, i.e. the Gamma function when offset to coincide with the factorial
  • the complete elliptic integral of the third kind
  • the fundamental groupoid
  • osmotic pressure
• ${\displaystyle \pi }$ represents:
  • Archimedes' constant (more commonly just called Pi), the ratio of a circle's circumference to its diameter
  • the prime-counting function
  • the state distribution of a Markov chain
  • in reinforcement learning, a policy function defining how a software agent behaves for each possible state of its environment
  • a type of covalent bond in chemistry (pi bond)
  • a pion (pi meson) in particle physics
  • in statistics, the population proportion
  • nucleotide diversity in molecular genetics
  • in electronics, a special type of small signal model is referred to as a hybrid-pi model
  • in discrete mathematics, a permutation
  • Projection
• ϖ (a graphic variant, see pomega) represents:
  • angular frequency of a wave, in fluid dynamics (angular frequency is usually represented by ${\displaystyle \omega }$ but this may be confused with vorticity in a fluid dynamics context)
  • longitude of pericenter, in astronomy ^[54]
  • comoving distance, in cosmology ^[55]

Ρρ (rho)

See also: Rho (disambiguation)

• ${\displaystyle \mathrm {P} }$ represents:
  • one of the Gegenbauer functions in analytic number theory (may be replaced by the capital form of the Latin letter P).
• ${\displaystyle \rho }$ represents:
  • one of the Gegenbauer functions in analytic number theory.
  • the Dickman–de Bruijn function
  • the radius in a polar, cylindrical, or spherical coordinate system
  • the correlation coefficient in statistics
  • the radius of convergence in real analysis ^[56]
  • the sensitivity to interest rate in mathematical finance
  • density (mass or charge per unit volume; may be replaced by the capital form of the Latin letter D) ^[57]
  • resistivity
  • the shape and reshape operators in APL (in the form ⍴)
  • the rename operator in relational algebra
  • the plastic ratio
  • Rho meson

Σσς (sigma)

See also: Sigma (disambiguation)

• ${\displaystyle \Sigma }$ represents:
  • the summation operator
  • the covariance matrix
  • the set of terminal symbols in a formal grammar
  • Mathematical surface
  • Sigma baryon
• ${\displaystyle \sigma }$ represents:
  • Stefan–Boltzmann constant in blackbody radiation ^{[58] [59]}
  • the divisor function in number theory
  • the real part of the complex variable ${\displaystyle s=\sigma +it}$ in analytic number theory
  • the sign of a permutation in the theory of finite groups
  • the population standard deviation, a measure of spread in probability and statistics
  • a type of covalent bond in chemistry (sigma bond)
  • the selection operator in relational algebra
  • stress in mechanics ^[60]
  • electrical conductivity
  • area density
  • Cross section
    • nuclear cross section
  • surface charge density for microparticles
  • standard deviation of a random variable in statistics
  • Spectrum of a matrix
  • Spin

Ττ (tau)

See also: Tau (disambiguation)

• ${\displaystyle \tau }$ represents:
  • torque, the net rotational force in mechanics
  • the elementary tau lepton in particle physics
  • a mean lifetime, of an exponential decay or spontaneous emission process
  • the time constant of any device, such as an RC circuit
  • proper time in relativity
  • one turn: the constant ratio of a circle's circumference to its radius, with value ${\displaystyle 2\pi }$ (6.283...). ^[61]
  • Kendall tau rank correlation coefficient, a measure of rank correlation in statistics
  • Ramanujan's tau function in number theory
  • shear stress in continuum mechanics ^[62]
  • a type variable in type theories, such as the simply typed lambda calculus
  • path tortuosity in reservoir engineering
  • in topology, a given topology
  • the tau in biochemistry, a protein associated to microtubules
  • the number of divisors of highly composite numbers (sequence A000005 in the OEIS )
  • precision (${\displaystyle \tau ^{2}}$), the reciprocal of variance, in statistics

ϒυ (upsilon)

See also: Upsilon (disambiguation)

• ${\displaystyle \Upsilon }$ (U+03D2) represents:
  • the upsilon meson

Φφ (phi)

See also: Phi (disambiguation)

• ${\displaystyle \Phi }$ represents:
  • the work function in physics; the energy required by a photon to remove an electron from the surface of a metal
  • magnetic flux or electric flux
  • the cumulative distribution function of the normal distribution in statistics
  • phenyl functional group in organic chemistry (pseudoelement symbol)
  • the reciprocal of the golden ratio (represented by ${\displaystyle \phi }$, below), also represented as ${\displaystyle 1/\phi }$
  • the value of the integration of information in a system (based on integrated information theory)
  • Geopotential
  • Alternative symbol for a wave function in quantum mechanics

Note: The empty set symbol ∅ looks similar, but is unrelated to the Greek letter.

• ${\displaystyle \phi }$ or ${\displaystyle \varphi }$ represents:
  • the golden ratio 1.618... in mathematics, art, and architecture ^[63]
  • Euler's totient function in number theory ^[64]
  • the argument of a complex number in mathematics
  • the value of a plane angle in physics and mathematics
  • the angle to the z axis in spherical coordinates (mathematics)
  • epoch or phase difference between two waves or vectors
  • the angle to the x axis in the xy-plane in spherical or cylindrical coordinates (physics)
  • latitude in geodesy
  • radiant flux
  • neutron flux
  • Potential energy
  • electric potential
  • a scalar field in quantum field theory
  • the probability density function of the normal distribution in statistics
  • the Veblen functions

Χχ (chi)

See also: Chi (disambiguation)

• ${\displaystyle \chi }$ represents:
  • the chi distribution in statistics (${\displaystyle \chi ^{2}}$ is the more frequently encountered chi-squared distribution)
  • the chromatic number of a graph in graph theory ^[65]
  • the Euler characteristic in algebraic topology ^[66]
  • electronegativity in the periodic table
  • the Fourier transform of a linear response function
  • a character in mathematics; especially a Dirichlet character in number theory
  • sometimes the mole fraction
  • a characteristic or indicator function in mathematics
  • the magnetic susceptibility of a material in physics ^[67]
  • the fission neutron energy spectrum in neutron transport

Ψψ (psi)

See also: Psi (disambiguation)

• ${\displaystyle \Psi }$ represents:
  • a quaternary combinator in combinatory logic
  • a symbol for psychology
  • the wave function in the Schrödinger equation of quantum mechanics ^[68]
• ${\displaystyle \psi }$ represents:
  • the J/psi mesons in particle physics
  • the stream function in fluid dynamics
  • the reciprocal Fibonacci constant ^[69]
  • the second Chebyshev function in number theory ^[70]
  • the polygamma function in mathematics ^[71]
  • the supergolden ratio ^[72]
  • In circadian physiology, ψ represents the phase relationship between a zeitgeber and a biological rhythm. ^[73]
  • In virology the ψ site is a viral packaging signal. ^[74]
  • Water potential in movement of water between plant cells. ^[75]

Ωω (omega)

See also: Omega (disambiguation)

• ${\displaystyle \Omega }$ represents:
  • Absolute infinite
  • the SI unit measure of electrical resistance, the ohm ^{[76] [77]}
  • the right ascension of the ascending node (RAAN) or Longitude of the ascending node in astronomy and orbital mechanics
  • the omega constant 0.5671432904097838729999686622... ^[78]
  • an asymptotic lower bound notation related to big O notation
  • in probability theory and statistical mechanics, the support
  • a solid angle ^{[79] [80]}
  • the omega baryon
  • the arithmetic function counting a number's prime factors counted with multiplicity
  • the density parameter in cosmology ^[81]
  • the first uncountable ordinal (also written as ω₁) ^[82]
  • Chaitin's constant for a given computer program
  • the vacuum state in quantum field theory
• ${\displaystyle \omega }$ represents:
  • angular velocity / radian frequency (rad/sec) ^[83]
  • the argument of periapsis in astronomy and orbital mechanics
  • a complex cube root of unity — the other is ${\displaystyle \omega ^{2}}$ — (used to describe various ways of calculating the discrete Fourier transform)
  • the differentiability class (i.e.${\displaystyle C^{\omega }}$) for functions that are infinitely differentiable because they are complex analytic
  • the first infinite ordinal
  • the omega meson
  • the set of natural numbers in set theory (although ${\displaystyle \mathbb {N} }$ or N is more common in other areas of mathematics)
  • an asymptotic dominant notation related to big O notation
  • in probability theory, a possible outcome of an experiment
  • the arithmetic function counting a number's distinct prime factors ^[84]
  • the symbol ϖ, a graphic variant of π, is sometimes construed as omega with a bar over it; see π
  • the unsaturated fats nomenclature in biochemistry (e.g. ω−3 fatty acids)
  • the first uncountable ordinal ${\displaystyle \omega _{1}}$ (also written as Ω)
  • the clique number (number of vertices in a maximum clique) of a graph in graph theory ^[85]

See also

• Blackboard bold letters used in mathematics
• English pronunciation of Greek letters
• Latin letters used in mathematics, science, and engineering
• List of letters used in mathematics, science, and engineering
• Glossary of mathematical symbols
• Mathematical Alphanumeric Symbols (a Unicode block)
• Mathematical notation
• Greek alphabet

References

1. Lindenmayer, David. (2005). Practical conservation biology. Burgman, Mark A. Collingwood, Vic.: CSIRO Pub. p. 404. ISBN   0-643-09310-9. OCLC   65216357. These parameters are related by the expression:… where E is effect size, n is sample size, α is the type I error rate and σ is the standard deviation of the variability of the data
2. "fine-structure constant". physics.nist.gov. Retrieved 2025-02-10.
3. Rabinowitz, Harold; Vogel, Suzanne (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam Burlington, MA: Elsevier/Academic Press. p. 348. ISBN   978-0-12-373980-3.
4. Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 793. ISBN   978-0-12-373980-3. OCLC   156811865.
5. Lamond, Joseph F.; Pielert, J. H., eds. (2006). Significance of tests and properties of concrete and concrete-making materials. STP (Rev. ed.). Philadelphia, PA: ASTM. p. 229. ISBN   978-0-8031-3367-9. OCLC   69865403. Thermal diffusivity is defined numerically as thermal conductivity divided by the product of specific heat and density, or α= k/ (CxP)
6. Burns, M. Shane (2022). A practical guide to observational astronomy (First ed.). Boca Raton: CRC Press. p. 5. ISBN   978-0-367-76863-8. The two angles that specify the location of a point on the celestial sphere are called the right ascension α and the declination δ
7. Rabinowitz, Harold; Vogel, Suzanne (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam Burlington, MA: Elsevier/Academic Press. p. 363. ISBN   978-0-12-373980-3. The primary designation system for bright stars, called Bayer designations… The Greek letters are assigned in order (α,β, γ,δ etc.) according to brightness.
8. Bhandari, Pritha (2021-01-18). "Type I & Type II Errors | Differences, Examples, Visualizations". Scribbr. Retrieved 2025-01-22. The probability of making a Type I error is the significance level, or alpha (α), while the probability of making a Type II error is beta (β).
9. Languis, M. L.; Buffer, James J.; Martin, Daniel; Naour, Paul J. (2011). Cognitive Science (RLE Edu E): Contributions to Educational Practice. Routledge Library Editions: Education. Hoboken: Taylor and Francis. p. 183. ISBN   978-0-415-68351-7. Vieth (1982) established that cognition could be quantified by summing the value of alpha plus beta brain waves.
10. Bowen, Alan C.; Rochberg, Francesca, eds. (2020). Hellenistic astronomy: the science in its contexts. Brill's companions in classical studies. Leiden ; Boston: Brill. pp. 16–17. ISBN   978-90-04-24336-1. Celestial longitude (λ) is measured eastward from the vernal equinox along the zodiacal circle, and celestial latitude (β) is the angular distance of the arc dropped perpendicularly from the body to the zodiacal circle.
11. Freidberg, Jeffrey P. (2014). Ideal MHD (1st ed.). West Nyack: Cambridge University Press. p. 68. ISBN   978-1-107-00625-6. The quantity β is a global plasma parameter whose value is critical for a fusion reactor... Qualitatively, β measures the ratio plasma pressure to magnetic pressure:
12. Volchenkov, Dimitri (2022). Mathematical Methods in Modern Complexity Science. Nonlinear Systems and Complexity Series. José António Tenreiro Machado. Cham: Springer International Publishing AG. p. 36. ISBN   978-3-030-79411-8. We defined β as the ratio v/c, where v the is the modulus of the vector velocity v.
13. Zhang, Keqian; Li, Dejie, eds. (2008). Electromagnetic Theory for Microwaves and Optoelectronics. SpringerLink Bücher (2nd ed.). Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg. p. 82. ISBN   978-3-540-74295-1. The reflection coefficient Γis real when medium 1 and medium 2 are both lossless media,…
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15. Hogg, Robert V.; Klugman, Stuart A. (2009). Loss Distributions. Wiley Series in Probability and Statistics. Hoboken: John Wiley & Sons, Inc. p. 225. ISBN   978-0-471-87929-9.
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17. Kahle, Reinhard; Rathjen, Michael (2020). The legacy of Kurt Schütte. Cham: Springer. p. 41. ISBN   978-3-030-49423-0. The Veblen approach was quite sufficient even for the ordinal, now known as the Feferman–Schütte ordinal, Γ₀ for predictive analysis
18. "DLMF: §5.2 Definitions ‣ Properties ‣ Chapter 5 Gamma Function". dlmf.nist.gov. Retrieved 2025-01-31.
19. Fayngold, Moses (2008). Special relativity and how it works. Physics textbook. Weinheim: Wiley-VCH. p. 32. ISBN   978-3-527-40607-4. Because we will come across this coefficient quite often, we will give it a special name, the Lorentz factor, and stick to our symbol γ(V),...
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21. Weisstein, Eric W. "Feigenbaum Constant". mathworld.wolfram.com. Retrieved 2025-01-23.
22. Weisstein, Eric W. "Delta Function". mathworld.wolfram.com. Retrieved 2025-01-23.
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30. Free, Rhona C. (2010). 21st century economics: a reference handbook. Thousand Oaks (Calif.): Sage. pp. 93–94. ISBN   978-1-4129-6142-4.
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32. Hunter, Robert J. (1988). Zeta potential in colloid science: principles and applications. Colloid science (New paperback ed.). London San Diego: Academic Press. p. 6. ISBN   978-0-12-361961-7. It is also possible to correlate the ζ-potential with the sedimentation behaviour of colloidal systems and with the flotation behaviour of mineral ores.
33. Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 346. ISBN   978-0-12-373980-3. OCLC   156811865.
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36. Rybicki, George B.; Lightman, Alan P. (1979). Radiative processes in astrophysics. A Wiley-Interscience publication. New York: Wiley. p. 123. ISBN   978-0-471-04815-2.
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38. Kubat, Miroslav (2021). An introduction to machine learning (Third ed.). Cham, Switzerland: Springer Nature. p. 129. ISBN   978-3-030-81934-7. When describing backpropagation of error, we assumed a constant learning rate, η .
39. Weisstein, Eric W. "Kappa Curve". mathworld.wolfram.com. Retrieved 2025-02-06.
40. Weisstein, Eric W. "Vertex Connectivity". mathworld.wolfram.com. Retrieved 2025-02-06.
41. Weisstein, Eric W. "Curvature". mathworld.wolfram.com. Retrieved 2025-02-06.
42. "Thermal Conductivity - Definition and Detailed Explanation". BYJUS. Retrieved 2025-02-06. It is generally denoted by the symbol 'k' but can also be denoted by 'λ' and 'κ'.
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46. Bowen, Alan C.; Rochberg, Francesca, eds. (2020). Hellenistic astronomy: the science in its contexts. Brill's companions in classical studies. Leiden ; Boston: Brill. pp. 16–17. ISBN   978-90-04-24336-1. Celestial longitude (λ) is measured eastward from the vernal equinox along the zodiacal circle, and celestial latitude (β) is the angular distance of the arc dropped perpendicularly from the body to the zodiacal circle.
47. "Vacuum magnetic permeability". physics.nist.gov. Retrieved 2025-02-10.
48. Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 333. ISBN   978-0-12-373980-3. OCLC   156811865.
49. Rabinowitz, Harold; Vogel, Suzanne (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam Burlington, MA: Elsevier/Academic Press. p. 346. ISBN   978-0-12-373980-3.
50. Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 347. ISBN   978-0-12-373980-3. OCLC   156811865.
51. Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 333. ISBN   978-0-12-373980-3. OCLC   156811865.
52. Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 346. ISBN   978-0-12-373980-3. OCLC   156811865.
53. Grossman, Nathaniel (1996). The Sheer Joy of Celestial Mechanics. Boston, MA: Birkhäuser Boston. p. 75. ISBN   978-0-8176-3832-0. Introduce variables ζ and η related to the true anomaly f and the eccentric anomaly E by…
54. Weisstein, Eric W. "Pomega -- from Eric Weisstein's World of Physics". scienceworld.wolfram.com. Retrieved 2022-09-06.
55. Outline for Weeks 14&15, Astronomy 225 Spring 2008 Archived 2010-06-15 at the Wayback Machine
56. Lebl, Jiří (May 16, 2022). Basic Analysis I, Introduction to Real Analysis. Vol. 1. p. 98. ISBN   978-1718862401.
57. Rabinowitz, Harold; Vogel, Suzanne (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam Burlington, MA: Elsevier/Academic Press. p. 346. ISBN   978-0-12-373980-3.
58. "CODATA Value: Stefan-Boltzmann constant". physics.nist.gov. Retrieved 2025-01-25.
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60. Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 346. ISBN   978-0-12-373980-3. OCLC   156811865.
61. Hartl, Michael (2010). "Tau Day – No, really, pi is wrong: The Tau Manifesto" . Retrieved 2015-03-20.
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63. Weisstein, Eric W. "Golden Ratio". mathworld.wolfram.com. Retrieved 2025-02-06.
64. Weisstein, Eric W. "Totient Function". mathworld.wolfram.com. Retrieved 2025-02-06.
65. Weisstein, Eric W. "Chromatic Number". mathworld.wolfram.com. Retrieved 2025-02-09. The chromatic number of a graph G is most commonly denoted χ (G) (e.g., Skiena 1990, West 2000, Godsil and Royle 2001, Pemmaraju and Skiena 2003),...
66. Weisstein, Eric W. "Euler Characteristic". mathworld.wolfram.com. Retrieved 2025-02-09.
67. Mugiraneza, Sam; Hallas, Alannah M. (2022-04-19). "Tutorial: a beginner's guide to interpreting magnetic susceptibility data with the Curie-Weiss law". Communications Physics. 5 (1): 1–12. doi:10.1038/s42005-022-00853-y. ISSN   2399-3650. However, for newly synthesized materials, there is one indispensable characterization technique that is as old as the field of magnetism itself: magnetic susceptibility, χ,...
68. Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 347. ISBN   978-0-12-373980-3. OCLC   156811865.
69. Weisstein, Eric W. "Reciprocal Fibonacci Constant". mathworld.wolfram.com. Retrieved 2025-02-08.
70. Weisstein, Eric W. "Chebyshev Functions". mathworld.wolfram.com. Retrieved 2025-02-08.
71. Weisstein, Eric W. "Polygamma Function". mathworld.wolfram.com. Retrieved 2025-02-08. A special function mostly commonly denoted ψ_n(z), ψ^((n))(z), or F_n(z-1)...
72. Crilly, Tony (1994). "A Supergolden Rectangle". The Mathematical Gazette. 78 (483): 320–325. doi:10.2307/3620208. JSTOR   3620208.
73. Srivastava, Manishi; Varma, Vishwanath; Abhilash, Lakshman; Sharma, Vijay Kumar; Sheeba, Vasu (June 2019). "Circadian Clock Properties and Their Relationships as a Function of Free-Running Period in Drosophila melanogaster". Journal of Biological Rhythms. 34 (3): 231–248. doi:10.1177/0748730419837767. ISSN   1552-4531. PMID   30939971. ... 2) accuracy (i.e., day-to-day stability of the phase relationship (ψ), where ψ is the duration between a phase of the rhythm and a phase of the external cycle) is greater for clocks with τ close to 24 h; ...
74. Rein, Alan (2020-07-28). "The heart of the HIV RNA packaging signal?". Proceedings of the National Academy of Sciences of the United States of America. 117 (33). doi:10.1073/pna. Archived from the original on 2025-01-03. vRNA is selectively packaged because it contains a "packaging signal" or "ψ" [also designated the "core encapsidation signal" (2)].
75. WELBAUM, GREGORY E.; BRADFORD, KENT J. (1991-03-01). "Water Relations of Seed Development and Germination in Muskmelon (Cucumis melo L.): VI. INFLUENCE OF PRIMING ON GERMINATION RESPONSES TO TEMPERATURE AND WATER POTENTIAL DURING SEED DEVELOPMENT". Journal of Experimental Botany. 42 (3): 393–399. doi:10.1093/jxb/42.3.393. ISSN   0022-0957. Germination sensitivities to temperature and water potential (ψ) were quantified as indicators of the influence of seed maturity and priming on seed vigour.
76. "Ohm | Electricity, Resistance & Voltage | Britannica". www.britannica.com. 2025-01-03. Retrieved 2025-02-08. ohm, abbreviation Ω, unit of electrical resistance in the metre-kilogram-second system,
77. Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 347. ISBN   978-0-12-373980-3. OCLC   156811865.
78. Weisstein, Eric W. "Omega Constant". mathworld.wolfram.com. Retrieved 2025-02-06.
79. Weisstein, Eric W. "Solid Angle". mathworld.wolfram.com. Retrieved 2025-02-07. The solid angle Ω subtended by a surface S is defined as the surface area Ω of a unit sphere covered by the surface's projection onto the sphere.
80. Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 346. ISBN   978-0-12-373980-3. OCLC   156811865.
81. "Density Parameter | COSMOS". astronomy.swin.edu.au. Retrieved 2025-02-07.
82. Weisstein, Eric W. "Ordinal Number". mathworld.wolfram.com. Retrieved 2025-02-06. The first transfinite ordinal, denoted ω ...
83. Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 346. ISBN   978-0-12-373980-3. OCLC   156811865.
84. Weisstein, Eric W. "Distinct Prime Factors". mathworld.wolfram.com. Retrieved 2025-02-06.
85. Weisstein, Eric W. "Clique". mathworld.wolfram.com. Retrieved 2025-02-07. A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique number ω(G)).

External links

• A pronunciation guide with audio
• Greek alphabet letters onclick copy paste