Results 31 to 40 of about 60,960 (218)
Limits of elliptic hypergeometric biorthogonal functions [PDF]
, 2011 The purpose of this article is to bring structure to (basic) hypergeometric biorthogonal systems, in particular to the q-Askey scheme of basic hypergeometric orthogonal polynomials.
Askey +15 more
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The c-function expansion of a basic hypergeometric function associated to root systems [PDF]
, 2014 We derive an explicit c-function expansion of a basic hypergeometric function associated to root systems. The basic hypergeometric function in question was constructed as explicit series expansion in symmetric Macdonald polynomials by Cherednik in case ...
Gasper +11 more
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Associated Basic Hypergeometric Series [PDF]
Proceedings of the Glasgow Mathematical Association, 1953 The purpose of the present note is to give some interesting and simple identities connected with basic hypergeometric series of the types 2Φ1 and 3Φ2.
openaire +2 more sources
Clausen's series 3F2(1) with integral parameter differences and transformations of the hypergeometric function 2F2(x) [PDF]
, 2012 We obtain summation formulas for the hypergeometric series 3 F 2(1) with at least one pair of numeratorial and denominatorial parameters differing by a negative integer.
Miller, A. R., Paris, Richard B.
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Қарағанды университетінің хабаршысы. Математика сериясыHypergeometric functions are divided into complete and confluent functions. Srivastava and Karlsson were the first to propose a method for constructing the complete set of triple Gaussian hypergeometric series and compiled a table containing definitions
A. Hasanov, T.G. Ergashev, A.R. Ryskan
doaj +1 more source
Extending Gaussian hypergeometric series to the $p$-adic setting
, 2012 We define a function which extends Gaussian hypergeometric series to the $p$-adic setting. This new function allows results involving Gaussian hypergeometric series to be extended to a wider class of primes.
Ahlgren S. +3 more
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On the supercongruence conjectures of van Hamme [PDF]
, 2015 In 1997, van Hamme developed $p-$adic analogs, for primes $p$, of several series which relate hypergeometric series to values of the gamma function, originally studied by Ramanujan.
Swisher, Holly
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A generalization of Clausen's identity
, 2009 The paper aims to generalize Clausen's identity to the square of any Gauss hypergeometric function. Accordingly, solutions of the related 3rd order linear differential equation are found in terms of certain bivariate series that can reduce to 3F2 series ...
G.E. Andrews +6 more
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Duality relations for hypergeometric series
, 2014 We explicitly give the relations between the hypergeometric solutions of the general hypergeometric equation and their duals, as well as similar relations for q-hypergeometric equations.
Beukers, Frits, Jouhet, Frédéric
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Elementary derivations of identities for bilateral basic hypergeometric series
, 2000 We give elementary derivations of several classical and some new summation and transformation formulae for bilateral basic hypergeometric series. For purpose of motivation, we review our previous simple proof ("A simple proof of Bailey's very-well-poised
Schlosser, M.
core +1 more source