In mathematics, the Narumi polynomialssn(x) are polynomials introduced by Narumi (1929) given by the generating function
( Roman 1984 , 4.4), ( Boas & Buck 1958 , p.37)
In mathematics, the Narumi polynomialssn(x) are polynomials introduced by Narumi (1929) given by the generating function
( Roman 1984 , 4.4), ( Boas & Buck 1958 , p.37)
In mathematics, the factorial of a non-negative integer , denoted by , is the product of all positive integers less than or equal to . The factorial of also equals the product of with the next smaller factorial:
A finite difference is a mathematical expression of the form f (x + b) − f (x + a). If a finite difference is divided by b − a, one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems.
In mathematics, a polynomial sequence, i.e., a sequence of polynomials indexed by non-negative integers in which the index of each polynomial equals its degree, is said to be of binomial type if it satisfies the sequence of identities
In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain shadowy techniques used to "prove" them. These techniques were introduced by John Blissard and are sometimes called Blissard's symbolic method. They are often attributed to Édouard Lucas, who used the technique extensively.
In mathematics, a Sheffer sequence or poweroid is a polynomial sequence, i.e., a sequence (pn(x) : n = 0, 1, 2, 3, ...) of polynomials in which the index of each polynomial equals its degree, satisfying conditions related to the umbral calculus in combinatorics. They are named for Isador M. Sheffer.
In mathematics, an Appell sequence, named after Paul Émile Appell, is any polynomial sequence satisfying the identity
A height function is a function that quantifies the complexity of mathematical objects. In Diophantine geometry, height functions quantify the size of solutions to Diophantine equations and are typically functions from a set of points on algebraic varieties to the real numbers.
In mathematics, a negligible function is a function such that for every positive integer c there exists an integer Nc such that for all x > Nc,
In mathematics the Mott polynomialssn(x) are polynomials introduced by N. F. Mott (1932, p. 442) who applied them to a problem in the theory of electrons. They are given by the exponential generating function
In mathematics the Gould polynomialsGn(x; a,b) are polynomials introduced by H. W. Gould and named by Roman in 1984. They are given by
In mathematics, Boas–Buck polynomials are sequences of polynomials defined from analytic functions and by generating functions of the form
In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product.
In mathematics, the Boole polynomialssn(x) are polynomials given by the generating function
In mathematics, the Pidduck polynomialssn(x) are polynomials introduced by Pidduck (1910, 1912) given by the generating function
In mathematics, the Peters polynomialssn(x) are polynomials studied by Peters (1956, 1956b) given by the generating function
In mathematics, Denisyuk polynomials Den(x) or Mn(x) are generalizations of the Laguerre polynomials introduced by Denisyuk (1954) given by the generating function
In mathematics, the actuarial polynomialsa(β)
n(x) are polynomials studied by Toscano (1950) given by the generating function
In mathematics, the Humbert polynomials πλ
n,m(x) are a generalization of Pincherle polynomials introduced by Humbert (1921) given by the generating function
In mathematics, the Rainville polynomialspn(z) are polynomials introduced by Rainville (1945) given by the generating function
Robert Creighton Buck, usually cited as R. Creighton Buck, was an American mathematician who, with Ralph Boas, introduced Boas–Buck polynomials. He taught at University of Wisconsin–Madison for 40 years. In addition, he was a writer.
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