Integral transforms and probability distributions involving a generalized hypergeometric function

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 F v p , q ; λ ; σ , τ u {{}_{u}F_{v}^{p,q;\lambda;\sigma,\tau}} of the generalized hypergeometric function F v u {{}_{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.

Some Generalized Properties of Poly-Daehee Numbers and Polynomials Based on Apostol–Genocchi Polynomials

“…Some of these functions were introduced to solve specific problems and some others were used to solve general problems. In recent years, generalized and multivariable forms of special functions of mathematical physics have also undergone significant evolutions (see [1][2][3][4][5][6][7][8][9][10][11][12] for more details). The theory of orthogonal polynomials and special functions is of intrinsic interest to many parts of mathematics.…”

Analytic solutions for vibrational energy levels of the pseudoharmonic potential

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