On some generalized integral transforms

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.

Applied Mathematics & Information Sciences

introduced the incomplete Pochhammer symbols that lead to a natural generalization and decomposition of a class of hypergeometric and other related functions to mainly investigate certain potentially useful closed-form representations of definite and semi-definite integrals of various special functions. Here, in this paper, we use the integral transforms like Beta transform, Laplace transform, Mellin transform, Whittaker transforms, K-transform and Hankel transform to investigate certain interesting and (potentially) useful integral transforms the incomplete hypergeometric type functions p γ q [z] and p Γ q [z]. Relevant connections of the various results presented here with those involving simpler and earlier ones are also pointed out.

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.

2010 AMS Mathematics Subject Classification: Primary: 33C20, 44A10, 44A45. Secondary: 33C05, 33C90. In this paper we intend to point out some minor typos which might have crept in inadvertently in four of the very recent results deduced by Kim and Lee [20] concerning the Laplace transforms of certain generalized hypergeometric functions pp F. We also augment their study [20] by presenting three additional results for which Kim and Lee [20] have stated the governing preliminary results in their introductory part of this paper [20] but the corresponding results flowing from these preliminary results have neither been stated nor deduced by them in the sequel. In this sense this study of ours augments the above mentioned investigations of Kim and Lee [20].

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.

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.

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.

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.

arXiv (Cornell University), 2023

In this work, we establish some Parseval-Goldstein type identities and relations that include various new generalized integral transforms such as Lα,µ-transform and generalized Stieltjes transform. In addition, we evaluated improper integrals of some fundamental and special functions using our results.

2020

In this study, known integral transforms such as Fourier and Hartley are studied and these integral transforms are studied in detail for bicomplex numbers. In addition, the properties of the bicomplex Hartley transform have been investigated. Also, the relation between Hartley and Fourier transform for bicomplex numbers is given.