Abstract.In this paper, the generalized Bessel matrix polynomials are introduced, starting from the hypergeometric matrix function. Integral form, Rodrigues’s formula and generating matrix function are then developed for the generalized Bessel matrix polynomials. These polynomials appear as finite series solutions of second-order matrix differential equations and orthogonality property for the ...

A bivariate gamma-type density function involving a confluent hypergeometric function of two variables is being introduced. The inverse Mellin transform technique is employed in conjunction with the transformation of variable technique to obtain its moment generating function, which is expressed in terms of generalized hypergeometric functions. Its cumulative distribution function is given in c...

Abstract The Laplace transform of the first exit time from a finite interval by a spectrally negative αstable Ornstein-Uhlenbeck process (1 < α ≤ 2) is provided in terms of the Wright’s generalized hypergeometric function 2Ψ1. The Laplace transform of first passage times is also derived for some related processes such as the process killed when it enters the negative half line and the process c...

The mathematical properties of the generalized hypergeometric function are now well established, due largely to the efforts of Bailey, Watson, Slater, and many others. There are available a number of books on the subject ['], [6] which contain extensive bibliographies together with an outline of the history of the investigations. A large portion of the published work concerning these functions ...

The objective of this paper is to define and study new generalized extended gamma functions. A generalized extended gamma probability density function involving generalized hypergeometric function is also defined. Closed form representations of the generalized gamma functions and the moment generating function are derived in the form of H-function using inverse Mellon transform techniques. Inco...

Dedicated to the memory of Professor Richard Askey (1933–2019) and pay tribute Bateman Project. Harry planned his “shoe-boxes” project (accomplished after death as Higher Transcendental Functions, Vols. 1–3, 1953–1955, under editorship by A. Erdélyi) a “Guide Functions”. This inspired author use modified title present survey. Most standard (classical) Special Functions are representable in term...

Integral inequalities for ?-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented via operator. A novel parameterized auxiliary identity involving proposed differentiable mappings. By identity, we derive several Ostrowski whose absolute values It that the obtained outcomes exhibit classical c...

Here, in this lecture, we aim at presenting a systematic account of the basic properties and characteristics of several subclasses of analytic functions (with Montel’s normalization), which are based upon some convolution operators on Hilbert space involving the Fox-Wright generalization of the classical hypergeometric qFs function (with q numerator and s denominator parameters). The various re...