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Extended hypergeometric and confluent hypergeometric functions
Applied Mathematics and Computation, 2004The functions under consideration are the extended Gaussian hypergeometric function \[ F_p(a,b;c,z)= {1\over B(b,c- b)} \int^1_0 t^{b-1}(1- t)^{c-b-1}(1- zt)^{-a}\exp\Biggl[-{p\over t(1- t)}\Biggr]\,dt \] and its confluent counterpart \(\Phi_p(b;c;z)\) with \(\exp(zt)\) in place of \((1- zt)^{-a}\). The authors discuss differentiation with respect to \(
Chaudhry, M. Aslam +3 more
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Extended Multivariable Hypergeometric Functions
2019In this chapter, we define an extension of multivariable hypergeometric functions. We obtain a generating function for these functions. Furthermore, we derive a family of multilinear and multilateral generating functions for these extended multivariable hypergeometric functions.
Erkuş-Duman, Esra, Düzgün, Düriye
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EXTENDED GENERALIZED τ -GAUSS’ HYPERGEOMETRIC FUNCTIONS AND THEIR APPLICATIONS
South East Asian J. of Mathematics and Mathematical Sciences, 2022In this article, by means of the extended beta function, we introduce new extension of the generalized τ -Gauss’ hypergeometric functions and present some new integral and series representations (including the one obtained by adopt- ing the well-known Ramanujan’s Master Theorem).
Chauhan, Bharti, Rai, Prakriti
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Extended symmetric Pascal matrices via hypergeometric functions
Applied Mathematics and Computation, 2004Cholesky's factorization of a symmetric, positive definite matrix has been studied recently in the context of factorizing the generalized Pascal and the symmetric Pascal matrices obtained from the Pascal triangle. The purpose of the paper is to get several positive definite matrices with the Cholesky triangles as the extended generalized Pascal ...
Cheon, Gi-Sang, El-Mikkawy, Moawwad
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Some Properties of Extended Hypergeometric Function and Its Transformations
Journal of the Indian Mathematical Society, 2018There emerges different extended versions of Beta function and hypergeometric functions containing extra parameters. We obtain some properties of certain functions like extended Generalized Gauss hypergeometric functions, extended Confluent hypergeometric functions including transformation formulas, Mellin transformation for the generalized extended ...
Chaturvedi, Aparna, Rai, Prakriti
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Certain Saigo Fractional Derivatives of Extended Hypergeometric Functions
2023This article aims to establish Saigo fractional derivatives of extended hypergeometric functions. Some special cases of these integrals are also derived.
S. Jain, R. Goyal, P. Agarwal, S. Momani
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Some results on the extended beta and extended hypergeometric functions
Applied Mathematics and Computation, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Luo, Min-Jie +2 more
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NEW GENERALIZATIONS OF EXTENDED BETA AND HYPERGEOMETRIC FUNCTIONS
Far East Journal of Theoretical Statistics, 2018Summary: Motivated by the generalizations of extended beta and hypergeometric functions, we introduce, in this paper, further generalizations of these functions. Some integral representations, properties, Mellin transformations, recurrence relations, and new statistical probability distributions are obtained for these new generalizations.
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Certain Pathway Fractional Integral Formulae Involving Extended Hypergeometric Functions
2023 International Conference on Fractional Differentiation and Its Applications (ICFDA), 2023Parik Laxmi +3 more
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Extended matrix variate hypergeometric function and its related functions
Bollettino dell'Unione Matematica ItalianaK. M. Bhammar, R. K. Jana
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