A Note on Natural Transformation of Exton’s Triple Series Hypergeometric Function (original) (raw)

Laplace transforms based some novel integrals via hypergeometric technique

arXiv (Cornell University), 2018

In this paper, we obtain the analytical solutions of Laplace transforms based some novel integrals with suitable convergence conditions, by using hypergeometric approach (some algebraic properties of Pochhammer symbol and classical summation theorems of hypergeometric series 2 F 1 (1), 2 F 1 (−1) , 4 F 3 (−1)). Also, we obtain the Laplace transforms of arbitrary powers of some finite series containing hyperbolic sine and cosine functions having different arguments, in terms of hypergeometric and Beta functions. Moreover, Laplace transforms of even and odd positive integral powers of sine and cosine functions with different arguments, and their combinations of the product (taking two, three, four functions at a time), are obtained. In addition, some special cases are yield from the main results.

A Study of Double Integral Transformation of Generalized Hypergeometric Function

IOSR Journal of Mathematics, 2013

In the present paper the authors will establish a double integral transform of Fox's H-function which leads to yet another interesting process of augmenting the parameters in the H-function. The result is of general character and on specializing the parameters suitably, yields several interesting results as particular cases.

A Study of Double Integral Transformation of Generalized Hypergeometric Function 1

In the present paper the authors will establish a double integral transform of Fox's H -function which leads to yet another interesting process of augmenting the parameters in the H -function. The result is of general character and on specializing the parameters suitably, yields several interesting results as particular cases.

Laplace Transform of Some Hypergeometric Functions

Nepal Journal of Mathematical Sciences

The hypergeometric functions are one of the most important and special functions in mathematics. They are the generalization of the exponential functions. Particularly the ordinary hypergeometric function 2F1(a, b; c; z) is represented by hypergeometric series and is a solution to a second order differential equation. Similarly, Laplace transform is a form of integral transform that converts linear differential equations to algebraic equations. This paper aims to study the convergence of hypergeometric function and Laplace transform of some hypergeometric functions. Moreover, some relationships between Laplace transformation and hypergeometric functions is established in the concluding section of this paper.

Some Integral Transforms and Fractional Integral Formulas for the Extended Hypergeometric Functions

Communications of the Korean Mathematical Society, 2016

Integral transforms and fractional integral formulas involving well-known special functions are interesting in themselves and play important roles in their diverse applications. A large number of integral transforms and fractional integral formulas have been established by many authors. In this paper, we aim at establishing some (presumably) new integral transforms and fractional integral formulas for the generalized hypergeometric type function which has recently been introduced by Luo et al. [9]. Some interesting special cases of our main results are also considered.

New Laplace Transforms for the Generalized Hypergeometric FUNCTION2F2

Honam Mathematical Journal, 2015

This paper is in continuation of the paper very recently published [New Laplace transforms of Kummer's confluent hypergeometric functions, Math. Comp. Modelling, 55 (2012), 1068-1071]. In this paper, our main objective is to show one can obtain so far unknown Laplace transforms of three rather general cases of generalized hypergeometric function 2 F 2 (x) by employing generalized Watson's, Dixon's and Whipple's summation theorems for the series 3 F 2 obtained earlier in a series of three research papers by Lavoie et al. [5, 6, 7]. The results established in this paper may be useful in theoretical physics, engineering and mathematics.

Some hypergeometric summation theorems and reduction formulas via Laplace transform method

Montes Taurus Journal of Pure and Applied Mathematics, 2018

In this paper, we obtain analytical solutions of Laplace transform based some generalized class of the hyperbolic integrals in terms of hypergeometric functions 3 F 2 (±1), 4 F 3 (±1), 5 F 4 (±1), 6 F 5 (±1), 7 F 6 (±1) and 8 F 7 (±1) with suitable convergence conditions, by using some algebraic properties of Pochhammer symbols. In addition, reduction formulas for 4 F 3 (1), 7 F 6 (−1) and some new summation theorems (not recorded earlier in the literature of hypergeometric functions) for 3 F 2 (−1), 6 F 5 (±1), 7 F 6 (±1) and 8 F 7 (±1) are obtained.

Some Integral Transforms Involving Extended Generalized Gauss Hypergeometric Functions

Communications of The Korean Mathematical Society, 2016

Using the extended generalized integral transform given by Luo et al. [6], we introduce some new generalized integral transforms to investigate such their (potentially) useful properties as inversion formulas and Parseval-Goldstein type relations. Classical integral transforms including (for example) Laplace, Stieltjes, and Widder-Potential transforms are seen to follow as special cases of the newly-introduced integral transforms.