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In mathematics, the q-Konhauser polynomials are a q-analog of the Konhauser polynomials. [1]
| | This article relies largely or entirely on a single source .(May 2024) |
In mathematics, the q-Konhauser polynomials are a q-analog of the Konhauser polynomials. [1]
In mathematics, a field F is algebraically closed if every non-constant polynomial in F[x] has a root in F.
In mathematics, a finite field or Galois field is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are given by the integers mod p when p is a prime number.
In mathematics, a polynomial is a mathematical expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate x is x2 − 4x + 7. An example with three indeterminates is x3 + 2xyz2 − yz + 1.
Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative rings include polynomial rings; rings of algebraic integers, including the ordinary integers ; and p-adic integers.
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K. In this case, one speaks of a rational function and a rational fraction over K. The values of the variables may be taken in any field L containing K. Then the domain of the function is the set of the values of the variables for which the denominator is not zero, and the codomain is L.
In mathematics, an algebraic function is a function that can be defined as the root of an irreducible polynomial equation. Algebraic functions are often algebraic expressions using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power. Examples of such functions are:
In mathematics, the Mahler measureof a polynomial with complex coefficients is defined as
In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. Specifically, it is an invariant of an oriented knot or link which assigns to each oriented knot or link a Laurent polynomial in the variable with integer coefficients.
Richard Allen Askey was an American mathematician, known for his expertise in the area of special functions. The Askey–Wilson polynomials are on the top level of the Askey scheme, which organizes orthogonal polynomials of hypergeometric type into a hierarchy. The Askey–Gasper inequality for Jacobi polynomials is essential in de Brange's famous proof of the Bieberbach conjecture.
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 the mathematical field of representation theory, a Kazhdan–Lusztig polynomial is a member of a family of integral polynomials introduced by David Kazhdan and George Lusztig. They are indexed by pairs of elements y, w of a Coxeter group W, which can in particular be the Weyl group of a Lie group.
Alan M. Frieze is a professor in the Department of Mathematical Sciences at Carnegie Mellon University, Pittsburgh, United States. He graduated from the University of Oxford in 1966, and obtained his PhD from the University of London in 1975. His research interests lie in combinatorics, discrete optimisation and theoretical computer science. Currently, he focuses on the probabilistic aspects of these areas; in particular, the study of the asymptotic properties of random graphs, the average case analysis of algorithms, and randomised algorithms. His recent work has included approximate counting and volume computation via random walks; finding edge disjoint paths in expander graphs, and exploring anti-Ramsey theory and the stability of routing algorithms.
In knot theory, the stevedore knot is one of three prime knots with crossing number six, the others being the 62 knot and the 63 knot. The stevedore knot is listed as the 61 knot in the Alexander–Briggs notation, and it can also be described as a twist knot with four half twists, or as the (5,−1,−1) pretzel knot.
In mathematics, Stieltjes–Wigert polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, for the weight function
Waleed Al-Salam was a mathematician who introduced Al-Salam–Chihara polynomials, Al-Salam–Carlitz polynomials, q-Konhauser polynomials, and Al-Salam–Ismail polynomials. He was a Professor Emeritus at the University of Alberta.
In mathematics, the Rogers polynomials, also called Rogers–Askey–Ismail polynomials and continuous q-ultraspherical polynomials, are a family of orthogonal polynomials introduced by Rogers in the course of his work on the Rogers–Ramanujan identities. They are q-analogs of ultraspherical polynomials, and are the Macdonald polynomials for the special case of the A1 affine root system.
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 Konhauser polynomials, introduced by Konhauser, are biorthogonal polynomials for the distribution function of the Laguerre polynomials.
In mathematics, the little q-Laguerre polynomialspn(x;a|q) or Wall polynomialsWn(x; b,q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme closely related to a continued fraction studied by Wall (1941). (The term "Wall polynomial" is also used for an unrelated Wall polynomial in the theory of classical groups.) Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.
Joseph D. E. Konhauser was an American mathematician who introduced Konhauser polynomials. He was a professor at Macalester College. He also organized many mathematical problems competitions. The annual Konhauser Problemfest is named after him.
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