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About 959 papers for “Generalized hypergeometric function”
B. M. Minton · Journal of Mathematical Physics · 1970
Two summation theorems are given for the terminating generalized hypergeometric function pFp−1, for arbitrary p, with certain restrictions on the parameters.
Cited by 75
Ganesh Bahadur Basnet, Narayan Prasad Pahari, Resham Prasad Paudel et al. · Nepal Journal of Mathematical Sciences · 2024
In this article, we have evaluated an integral involving a generalized hypergeometric function. This is achieved by employing a summation formula for the series 4F3 obtained earlier by Choi and Rathie [3]. A few special cases have also been given. The result provided in this note is simple, interesting, easily established, and may be useful. 2020 Mathematical subject classification: Primary: 05A15, 33C05, Secondary: 33C15, 33C20
Cited by 0Open access
Castillo Pérez, Jaime · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · 2008
Recently Virchenko and collaborators discussed a generalization of the function (see article pdf) where 2R1 (a, b; c;; x) is the generalized hypergeometric function presented by Dotsenko in 1991. The purpose of this article is to obtain some results that involve cases specials of this function and obtain computable forms for them.
Cited by 0Open access
Komal Singh Yadav, Bhagwat Sharan, Ashish Verma · Analysis · 2024
Abstract We introduce new extension of the extended Pochhammer symbol and gamma function by using the extended Mittag-Leffler function. We also present extension of the generalized hypergeometric function as well as some of their special cases by using this extended Pochhammer symbol. Further, we define the extension of the τ-Gauss hypergeometric function. Integral and derivative formulas involving the Mellin transform and fractional calculus techniques associated with this extended τ-Gauss hypergeometric function are also given. Also, new extended τ-Gauss hypergeometric function also provides a few more interesting and well-known results. This enriches the theory of special functions. The obtained results are believed to be newly presented.
Cited by 0
Н. А. Вирченко, S. L. Kalla, A. Al-Zamel · Integral Transforms and Special Functions · 2001
Recently Al-Musallam and S.L. Kalla [1], [2] have developed a generalized hypergeometric function occuring in diffraction theory. We define here a new generalized hypergeometric function, using a special case of Wright's function. Some differential properties, integral representations and special cases are given. Corresponding incomplete generalized gamma function and its complementary function are also defined and some properties are obtained. The hypergeometric function 2R1 (a, b; c; τ; z) is revisited to obtain more properties, including contiguous relations, differential formulas and integral representations. Results given earlier by Al-Musallam and Kalla, Kobayashi and some classical results of incomplete gamma functions can be recovered from some results derived in this paper
Cited by 77
Dmitrii Karp, С. М. Ситник · Victoria University Research Repository (Victoria University) · 2007
We find two-sided inequalities for the generalized hypergeometric function with positive parameters restricted by certain additional conditions. Inequalities are derived as corollaries of a theorem asserting the monotony of the quotient of two generalized hypergeometric functions with shifted parameters. The proofs hinge on a generalized Stieltjes representation of the generalized hypergeometric function. In the last section of the paper we list some open questions and conjectures.
Cited by 9
Bujar Xh. Fejzullahu · Integral Transforms and Special Functions · 2017
In this paper, the parameter derivatives to any order of the generalized hypergeometric function as well as for its various special cases are obtained.
Cited by 9
Y. Matsuhira, H. Nagoya · arXiv (Cornell University) · 2019
We solve connection problem between fundamental solutions at singular points $0$ and $1$ for the generalized hypergeometric function, using analytic continuation of the integral representation. All connection coefficients are products of the sine and the cosecant.
Cited by 0Open access
P. C. Munot, Pasumarthi A. Padmanabham · SHILAP Revista de lepidopterología · 2011
The object of the present paper is to establish a general expansion formula, which provides us a generating function for the generalized hypergeometric polynomials .
Cited by 0Open access
A. Kazarnovski-Krol · Birkhäuser Boston eBooks · 1997
Value of generalized hypergeometric function at a special point is calculated. More precisely, the value of certain multiple integral over vanishing cycle (all arguments collapse to unity) is calculated. The answer is expressed in terms of Γ-functions. The constant is relevant to the part of ρ in the Gindikin-Karpelevich formula for the c-function of Harish-Chandra. Calculation is an adaptation of classical calculations of Gelfand and Naimark (1950) to the Heckman-Opdam hypergeometric functions in the case of root system of type A n−1.
Cited by 4
Yudell L. Luke · Elsevier eBooks · 1975
Cited by 0
K. K. Chaudhary, S. B. Rao · Researches in Mathematics · 2024
This research article explores some new properties of generalized hypergeometric function and its q-analogue. The connections between ${}_{2}{{R}_{1}}^{\upsilon }(\mathfrak{z})$, the Wright function, and generalized Mittag-Leffler functions are explored. The authors introduce the q-analogue of generalized hypergeometric function denoted by ${}_{2}{{R}_{1}}^{\upsilon ,q}(\mathfrak{z})$ and discuss its properties and connections with q-Wright function and q-versions of generalized Mittag-Leffler functions. We get the q-integral transforms such as q-Mellin, q-Euler (beta), q-Laplace, q-sumudu, and q-natural transforms of Wright-type generalized q-hypergeometric function. This article contributes to the understanding of hypergeometric functions in q-calculus.
Cited by 0Open access
Dspace Repository (Marmara Üniversitesi) · 2020
The aim of this paper is to establish a general definite integrals involving product of the Aleph function and generalized incomplete hypergeometric function with general arguments. Being unified and general in nature, this integral yield a number of known and new results as special cases. For the sake of illustration, several corollaries are also recorded here as special case of our main results. ©Işık University, Department of Mathematics, 2021; all rights reserved.
Cited by 0
D Suthar, H Habenom, H Tadesse et al. · Acta Universitatis Apulensis · 2017
The aim of this paper is to establish certain integrals involving product of the Aleph function with exponential function and Fox-Wright's Generalized Hypergeometric Function. Being unified and general in nature, these integrals yield a number of known and new results as special cases. For the sake of illustration, four corollaries are also recorded here as special case of our main results.
Cited by 3Open access
N. Srimannarayana, B. Satyanarayana, D. Ramesh et al. · International Journal of Recent Technology and Engineering (IJRTE) · 2019
The subject of Special functions has a lot importance during the last few decades. The intend of this work is to test the convergence and to introduce the extended linear generating relation for the generalized hypergeometric function. The result is followed by its applications to the classical polynomials.
Cited by 1Open access
J. Patel, Namrata Pandey · International Journal of Apllied Mathematics · 2016
In the present paper, the authors establish some fractional integral and fractional derivative formulas involving a generalized confluent type hypergeometric function introduced by Parmer [6].
Cited by 0Open access
Ankit Pal, Kiran Kumari · Physica Scripta · 2023
Abstract This article deals with the representation of Dirichlet averages of the generalized confluent hypergeometric function (also referred to as a Mittag-Leffler-confluent hypergeometric function), which are presented by means of the Pathway fractional integral operator and of the generalized hypergeometric functions of multiple variables. Additionally, certain particular cases are taken into account when the aforementioned Dirichlet averages coincide with the confluent hypergeometric function and generalized Wright hypergeometric functions.
Cited by 1Open access
N. Srimannarayana, M. V. ChakradharaRao, M. Radha Madhavi et al. · AIP conference proceedings · 2023
Cited by 0
Dinesh Kumar, Frédéric Ayant, Faruk Uçar · TWMS Journal of Applied and Engineering Mathematics · 2019
The aim of this paper is to establish a general de finite integrals involving product of the Aleph function and generalized incomplete hypergeometric function with general arguments. Being unifi ed and general in nature, this integral yields a number of known and new results as special cases. For the sake of illustration, several corollaries are also recorded here as special case of our main results.
Cited by 1Open access
N. Srimannarayana, B. Satyanarayana, D. Ramesh · International Journal of Recent Technology and Engineering (IJRTE) · 2019
In previous papers, it has been introduced a generalized hypergeometric function of two variables. The present paper aims at to derive different types of integral representations for the generalized hypergeometric function. The results derived here are very general in nature and are interesting and can obtain some known and new integrals for various polynomials. Each result is followed by its applications to the classical orthogonal polynomials.
Cited by 3Open access