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Beyond the Gaussian.

Fujii, Kazuyuki (2011)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Bi-axial Gegenbauer functions of the first and second kind

Alan Common (1996)

Banach Center Publications

The classical orthogonal polynomials defined on intervals of the real line are related to many important branches of analysis and applied mathematics. Here a method is described to generalise this concept to polynomials defined on higher dimensional spaces using Bi-Axial Monogenic functions. The particular examples considered are Gegenbauer polynomials defined on the interval [-1,1] and the Gegenbauer functions of the second kind which are weighted Cauchy integral transforms over this interval of...

Binomial residues

Eduardo Cattani, Alicia Dickenstein, Bernd Sturmfels (2002)

Annales de l’institut Fourier

A binomial residue is a rational function defined by a hypergeometric integral whose kernel is singular along binomial divisors. Binomial residues provide an integral representation for rational solutions of A -hypergeometric systems of Lawrence type. The space of binomial residues of a given degree, modulo those which are polynomial in some variable, has dimension equal to the Euler characteristic of the matroid associated with A .

Binomial sums via Bailey's cubic transformation

Wenchang Chu (2023)

Czechoslovak Mathematical Journal

By employing one of the cubic transformations (due to W. N. Bailey (1928)) for the 3 F 2 ( x ) -series, we examine a class of 3 F 2 ( 4 ) -series. Several closed formulae are established by means of differentiation, integration and contiguous relations. As applications, some remarkable binomial sums are explicitly evaluated, including one proposed recently as an open problem.

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