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Properties of generalized univariate hypergeometric functions [PDF]

Communications in Mathematical Physics, 2006
Based on Spiridonov's analysis of elliptic generalizations of the Gauss hypergeometric function, we develop a common framework for 7-parameter families of generalized elliptic, hyperbolic and trigonometric univariate hypergeometric functions.
B. Nassrallah, D.P. Gupta, E. Koelink, E. Koelink, E. Koelink, E. M. Rains, F. J. van de Bult, F.J. Bult van de, G. Gasper, G. Letzter, J. V. Stokman, J.F. Diejen van, J.V. Stokman, J.V. Stokman, M. Noumi, M. Put van der, M. Rahman, M.E.H. Ismail, S. Lievens, S.N.M. Ruijsenaars, S.N.M. Ruijsenaars, S.N.M. Ruijsenaars, S.N.M. Ruijsenaars, T. Shintani, V.P. Spiridonov, V.P. Spiridonov, W. Groenevelt, Y. Komori   +27 more
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Some properties of generalized hypergeometric Appell polynomials [PDF]

Karpatsʹkì Matematičnì Publìkacìï, 2020
Let $x^{(n)}$ denotes the Pochhammer symbol (rising factorial) defined by the formulas $x^{(0)}=1$ and $x^{(n)}=x(x+1)(x+2)\cdots (x+n-1)$ for $n\geq 1$.
L. Bedratyuk, N. Luno
doaj   +4 more sources

Generalized Gamma, Beta and Hypergeometric Functions Defined by Wright Function and Applications to Fractional Differential Equations

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
doaj   +1 more source

On some new inequalities and fractional kinetic equations associated with extended gauss hypergeometric and confluent hypergeometric function

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
doaj   +1 more source

Implementation of summation theorems of Andrews and Gessel-Stanton

Қарағанды университетінің хабаршысы. Математика сериясы, 2023
Generalized hypergeometric functions and their natural generalizations in one and several variables appear in many mathematical problems and their applications.
M.I. Qureshi, T.R. Shah
doaj   +1 more source

Analytical expression for the exact curved surface area and volume of hyperboloid of two sheets via Mellin-Barnes type contour integration [PDF]

Journal of Mahani Mathematical Research, 2023
In this article, we aim at obtaining the analytical expression (not previously found and recorded in the literature) for the exact curved surface area of a hyperboloid of two sheets in terms of Appell's double hypergeometric function of second kind and ...
M.A. Pathan, M. Qureshi, Javid Majid
doaj   +1 more source

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, Rathie, Arjun K., Parmar, Rakesh K., Kim, Young Sup   +3 more
openaire   +2 more sources

Applications of q-difference equation and homogeneous q-shift operator rΦs(Dxy) in q-polynomials

Partial Differential Equations in Applied Mathematics, 2023
In this paper, the generalized homogeneous q-shift operator is constructed. The q-difference equation is then utilized to construct numerous polynomial q-identities, such as the generating function and its extension, Rogers’ formula and its extension ...
Samaher A. Abdul-Ghani, Husam L. Saad
doaj   +1 more source

Applications of Lehmer’s Infinite Series Involving Reciprocals of the Central Binomial Coefficients

Journal of Function Spaces, 2022
The main objective of this paper is to establish several new closed-form evaluations of the generalized hypergeometric function Fq+1qz for q=2,3,4,5. This is achieved by means of separating the generalized hypergeometric function Fq+1qz (q=2,3,4,5) into ...
B. R. Srivatsa Kumar, Adem Kılıçman, Arjun K. Rathie   +2 more
doaj   +1 more source

ON A NEW GENERALIZED BETA FUNCTION DEFINED BY THE GENERALIZED WRIGHT FUNCTION AND ITS APPLICATIONS

Malaysian Journal of Computing, 2021
Various extensions of classical gamma, beta, Gauss hypergeometric and confluent hypergeometric functions have been proposed recently by many researchers. In this paper, further generalized extended beta function with some of its properties like summation
Umar Muhammad Abubakar, Saroj Patel
doaj   +1 more source