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Some Summation Theorems for Generalized Hypergeometric Functions
Axioms, 2018 Essentially, whenever a generalized hypergeometric series can be summed in terms of gamma functions, the result will be important as only a few such summation theorems are available in the literature. In this paper, we apply two identities of generalized
Mohammad Masjed-Jamei, Wolfram Koepf
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A New Identity for Generalized Hypergeometric Functions and Applications
Axioms, 2019 We establish a new identity for generalized hypergeometric functions and apply it for first- and second-kind Gauss summation formulas to obtain some new summation formulas. The presented identity indeed extends some results of the recent published paper (
Mohammad Masjed-Jamei, Wolfram Koepf
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ON CONTIGUITY RELATIONS FOR GENERALIZED HYPERGEOMETRIC FUNCTIONS
Проблемы анализа, 2018 We derive formulas that generalize contiguity relations of Gauss hypergeometric functions to the case of hypergeometric functions satisfying differential equations of arbitrary order and also of solution matrices of their corresponding homogeneous ...
V. A. Gorelov
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A new generalization of generalized hypergeometric functions
Le Matematiche, 1997 In this paper a natural generalization of the familiar H -function of Fox namely the I -function is proposed. Convergence conditions, various series representations, elementary properties and special cases for the I -function have also been given.
Arjun K. Rathie
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Cumhuriyet Science Journal, 2022 When the literature is examined, it is seen that there are many studies on the generalizations of gamma, beta and hypergeometric functions. In this paper, new types of generalized gamma and beta functions are defined and examined using the Wright ...
Enes Ata, İ. Onur Kıymaz
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Symmetry, 2022 There have been numerous investigations on the hypergeometric series 2F1 and the generalized hypergeometric series pFq such as differential equations, integral representations, analytic continuations, asymptotic expansions, reduction cases, extensions of one and several variables, continued fractions, Riemann’s equation, group of the hypergeometric ...
Mohd Idris Qureshi +2 more
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International Journal of Mathematics for Industry, 2023 Fractional kinetic equations are of immense importance in describing and solving numerous intriguing problems of physics and astrophysics. Inequalities are important topics in special functions.
Ankita Chandola, Rupakshi Mishra Pandey
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GENERALIZATION OF EXTENDED BETA FUNCTION, HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS [PDF]
Honam Mathematical Journal, 2011 Summary: The main object of this paper is to present generalization of extended beta function, extended hypergeometric and confluent hypergeometric function introduced by Chaudhry et al. and obtained various integral representations, properties of beta function, Mellin transform, beta distribution, differentiation formulas, transform formulas ...
Lee, Dong Myung +3 more
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On the Algebraic Independence of the Values of Functions Associated with Hypergeometric Functions
Axioms, 2022 Functions that are integrals of products of generalized hypergeometric functions of some kind are considered. The conditions for the representability of these functions as a polynomial in hypergeometric ones are found.
Vasily Gorelov
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Degenerate binomial coefficients and degenerate hypergeometric functions
Advances in Difference Equations, 2020 In this paper, we investigate degenerate versions of the generalized pth order Franel numbers which are certain finite sums involving powers of binomial coefficients.
Taekyun Kim +3 more
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