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The main goal of this paper is to derive a number of identities for the generalized hypergeometric function evaluated at unity and for certain terminating multivariate hypergeometric functions from the symmetries and other properties of…

Classical Analysis and ODEs · Mathematics 2021-11-09 Asena Çetinkaya , Dmitrii Karp , Elena Prilepkina

We describe a new approach to the notion of general hypergeometric functions

Algebraic Geometry · Mathematics 2007-05-23 Israel M. Gelfand , Mark I. Graev

Kamp\'e de F\'eriet hypergeometric functions are two-variable hypergeometric functions, which are a generalization of Appell's functions. It is known that they satisfy many reduction and summation formulas. In this paper, we define Kamp\'e…

Number Theory · Mathematics 2023-06-13 Ryojun Ito , Satoshi Kumabe , Akio Nakagawa , Yusuke Nemoto

As a generalization of Riemann-Liouville integral, we introduce integral transformations of convergent power series which can be applied to hypergeometric functions with several variables.

Classical Analysis and ODEs · Mathematics 2023-11-16 Toshio Oshima

This paper presents the construction of a new set of generalized photon-added coherent states related to associated hypergeometric functions introduced in our previous work (Hounkonnou M N and Sodoga K, 2005, J. Phys. A: Math. Gen 38,…

Mathematical Physics · Physics 2018-11-14 K. Sodoga , I. Aremua , M. N. Hounkonnou

Classical Stieltjes Transform is modified in a way to generalize both Stieltjes and Fourier transforms. This transform allows to intro- duce new classes of commutative and non-commutative generalized convolutions. Key words: Stieltjes…

Probability · Mathematics 2016-10-04 Lev B Klebanov , Rasool Roozegar

The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral version of…

Classical Analysis and ODEs · Mathematics 2024-01-31 Giuseppe Dattoli , Mehnaz Haneef , Subuhi Khan , Silvia Licciardi

A certain special function of the generalized hypergeometric variety is shown to fulfill a host of useful noncommutative identities.

Quantum Algebra · Mathematics 2015-06-26 A. Yu. Volkov

Several integrals involving powers and ordinary hypergeometric functions are rederived by means of a generalized hypergeometric function of two variables (Appell's function) recovering some well-known expressions as particular cases. Simple…

High Energy Physics - Phenomenology · Physics 2007-05-23 M. A. Sanchis-Lozano

Approximation of entire functions by their pad\'e approximants has been examined in the past. It is true that generically such an approximation holds. However, examining this problem from another viewpoint, we obtain stronger generic…

Complex Variables · Mathematics 2011-05-17 G. Fournodavlos

We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…

Number Theory · Mathematics 2026-04-22 Akio Nakagawa

In this paper, we study some extended hypergeometric functions from matrix point of view. We have given the integral representations of these matrix functions. Finally, we obtain some generating function relations using fractional…

Classical Analysis and ODEs · Mathematics 2020-11-03 Ashish Verma , Ravi Dwivedi , Vivek Sahai

This paper is devoted for the study of a new generalization of Struve function type. In this paper , We establish four new integral formulas involving the Galue type Struve function, which are express in term of the generalized (Wright)…

Classical Analysis and ODEs · Mathematics 2016-08-11 D. L. Suthar , S. D. Purohit , K. S. Nisar

In these lecture notes I give an elementary introduction to elliptic hypergeometric functions. I focus on motivating the main ideas and constructions, rather than giving a comprehensive survey. The lectures include a brief explanation of…

Classical Analysis and ODEs · Mathematics 2017-06-21 Hjalmar Rosengren

The paper studies logarithmic convexity and concavity of the generalized hypergeometric function with respect to simultaneous shift of several parameters. We use integral representations and properties of Meijer's $G$ function to prove…

Classical Analysis and ODEs · Mathematics 2016-11-22 S. I. Kalmykov , D. B. Karp

The paper classifies algebraic transformations of Gauss hypergeometric functions with the local exponent differences $(1/2,1/4,1/4)$, $(1/2,1/3,1/6)$ and $(1/3,1/3,1/3)$. These form a special class of algebraic transformations of Gauss…

Classical Analysis and ODEs · Mathematics 2008-12-01 Raimundas Vidunas

In this work, we establish some Parseval-Goldstein type identities and relations that include various new generalized integral transforms such as $\mathcal{L}_{\alpha,\mu}$-transform and generalized Stieltjes transform. In addition, we…

Classical Analysis and ODEs · Mathematics 2023-09-26 Durmuş Albayrak

Methods of Pad\'e approximation are used to analyse a multivariate Markov transform which has been recently introduced by the authors, and which is generalizing the well-known in Spectral theory Stieltjes transform (Markov function) of…

Numerical Analysis · Mathematics 2011-12-07 Ognyan Kounchev , Hermann Render

In this article we obtain new irrationality measures for values of functions which belong to a certain class of hypergeometric functions including shifted logarithmic functions, binomial functions and shifted exponential functions. We…

Number Theory · Mathematics 2023-10-12 Makoto Kawashima , Anthony Poëls

This paper explores the calculus of dual-valued functions and investigates the gamma function, beta function and generalized hypergeometric functions by incorporating dual numbers as parameters and variables. We examine its fundamental…

General Mathematics · Mathematics 2025-07-29 Ravi Dwivedi , Juan Carlos Cortés