Results 31 to 40 of about 135,153 (239)
A General Family of q-Hypergeometric Polynomials and Associated Generating Functions
Mathematics, 2021 Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas of ...
Hari Mohan Srivastava, Sama Arjika
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Multiple big q-Jacobi polynomials [PDF]
Bulletin of Mathematical Sciences, 2020 Here, we investigate type II multiple big q-Jacobi orthogonal polynomials. We provide their explicit formulae in terms of basic hypergeometric series, raising and lowering operators, Rodrigues formulae, third-order q-difference equation, and we obtain ...
Fethi Bouzeffour, Mubariz Garayev
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New double-sum expansions for certain Mock theta functions
AIMS Mathematics, 2022 The study of expansions of certain mock theta functions in special functions theory has a long and quite significant history. Motivated by recent correlations between q-series and mock theta functions, we establish a new q-series transformation formula ...
Qiuxia Hu +3 more
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Some q-Supercongruences from Transformation Formulas for Basic Hypergeometric Series [PDF]
Constructive approximation, 2018 Several new q -supercongruences are obtained using transformation formulas for basic hypergeometric series, together with various techniques such as suitably combining terms, and creative microscoping, a method recently developed by the first author in ...
Victor J. W. Guo, M. Schlosser
semanticscholar +2 more sources
Hypergeometric Solutions of the $A_4^{(1)}$-Surface $q$-Painlev\'e IV Equation [PDF]
, 2014 We consider a $q$-Painlev\'e IV equation which is the $A_4^{(1)}$-surface type in the Sakai's classification. We find three distinct types of classical solutions with determinantal structures whose elements are basic hypergeometric functions. Two of them
Nakazono, Nobutaka
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The Bateman Functions Revisited after 90 Years—A Survey of Old and New Results
Mathematics, 2021 The Bateman functions and the allied Havelock functions were introduced as solutions of some problems in hydrodynamics about ninety years ago, but after a period of one or two decades they were practically neglected. In handbooks, the Bateman function is
Alexander Apelblat +2 more
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Some relations on Humbert matrix polynomials [PDF]
Mathematica Bohemica, 2016 The Humbert matrix polynomials were first studied by Khammash and Shehata (2012). Our goal is to derive some of their basic relations involving the Humbert matrix polynomials and then study several generating matrix functions, hypergeometric matrix ...
Ayman Shehata
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scCompass: An Integrated Multi-Species scRNA-seq Database for AI-Ready. [PDF]
Adv Sci (Weinh)scCompass integrates and standardizes transcriptomic data from ≈105 million single cells across 13 species, enabling the identification of stable expression genes and organ‐specific expression genes in humans and mice. It provides scalable datasets for AI model training, pretrained model checkpoints, and user‐friendly platforms for data sharing ...
Wang P +29 more
europepmc +2 more sources
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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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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