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Extended hypergeometric and confluent hypergeometric functions
The 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 \(
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Integral transforms and probability distributions involving a generalized hypergeometric function
Georgian Mathematical Journal, 2021Various extensions of the beta function together with their associated extended hypergeometric and confluent hypergeometric functions have been introduced and investigated.
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ON SOME EXTENDED SPECIAL FUNCTIONS WITH THE BI-FOX-WRIGHT FUNCTION KERNEL
JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES, 2023In the present article, our main goal is to study the new extended beta, Gauss and confluent hypergeometric functions defined by using the two Fox-Wright functions as their kernel.
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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 ...
Aparna Chaturvedi, Prakriti Rai
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Generalized Extended Confluent, Whittaker $k$-functions and Their Properties
European Journal of Pure and Applied MathematicsThe main objective of this research paper is to explore further generalization of confluent hypergeometric and Whittaker functions by introducing a new parameter $k>0$, in generalized extended confluent hypergeometric and Whittaker functions defined by ...
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