Title: Integral transforms and probability distributions involving a generalized hypergeometric function
Abstract: Abstract Various extensions of the beta function together with their associated extended hypergeometric and confluent hypergeometric functions have been introduced and investigated. In this paper, using the very recently contrived extended beta function, we aim to introduce an extension <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mmultiscripts> <m:mi>F</m:mi> <m:mi>v</m:mi> <m:mrow> <m:mi>p</m:mi> <m:mo>,</m:mo> <m:mi>q</m:mi> <m:mo>;</m:mo> <m:mi>λ</m:mi> <m:mo>;</m:mo> <m:mi>σ</m:mi> <m:mo>,</m:mo> <m:mi>τ</m:mi> </m:mrow> <m:mprescripts /> <m:mi>u</m:mi> <m:none /> </m:mmultiscripts> </m:math> {{}_{u}F_{v}^{p,q;\lambda;\sigma,\tau}} of the generalized hypergeometric function <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mmultiscripts> <m:mi>F</m:mi> <m:mi>v</m:mi> <m:none /> <m:mprescripts /> <m:mi>u</m:mi> <m:none /> </m:mmultiscripts> </m:math> {{}_{u}F_{v}} and investigate certain classes of transforms and several identities of a generalized probability distribution involving this extension. In fact, we present some interesting formulas of Jacobi, Gegenbauer, pathway, Laplace, and Legendre transforms of this extension multiplied by a polynomial. We also introduce a generalized probability distribution to investigate its several related properties. Further, we consider some special cases of our main results with an argument about the derived process of a known result.
Publication Year: 2021
Publication Date: 2021-07-28
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 4
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