• East Asian mathematical journal
• /
• v.15 no.2
• /
• pp.201-210
• /
• 1999

Morley provided an interesting identity about 20 years earlier before its more generalized form was given by Dixon. In this note some of its generalized forms and an application of Morley's formula are considered.

• Honam Mathematical Journal
• /
• v.35 no.4
• /
• pp.701-706
• /
• 2013

Summation theorems for hypergeometric series $_2F_1$ and generalized hypergeometric series $_pF_q$ play important roles in themselves and their diverse applications. Some summation theorems for $_2F_1$ and $_pF_q$ have been established in several or many ways. Here we give a proof of Watson's classical summation theorem for the series $_3F_2$(1) by following the same lines used by Rakha [7] except for the last step in which we applied an integral formula introduced by Choi et al. [3].

• Honam Mathematical Journal
• /
• v.32 no.4
• /
• pp.581-592
• /
• 2010

With the help of some techniques based upon certain inverse pairs of symbolic operators initiated by Burchnall-Chaundy, the authors investigate decomposition formulas associated with Saran's function $F_E$ in three variables. Many operator identities involving these pairs of symbolic operators are first constructed for this purpose. By employing their decomposition formulas, we also present a new group of integral representations for the Saran function $F_E$.

• East Asian mathematical journal
• /
• v.18 no.1
• /
• pp.111-125
• /
• 2002

Many different families of infinite series were recently observed to be summable in closed forms by means of certain operators of fractional calculus(that is, calculus of integrals and derivatives of any arbitrary real or complex order). In this sequel to some of these recent investigations, the authors present yet another instance of applications of certain fractional calculus operators. Alternative derivations without using these fractional calculus operators are shown to lead naturally a family of analogous infinite sums involving hypergeometric functions.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.4
• /
• pp.679-689
• /
• 2010

By developing and using certain operators like those initiated by Burchnall-Chaundy, the authors aim at investigating several decomposition formulas associated with the $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function $F_{2:0;0}^{0:3;3}$ [x, y]. For this purpose, many operator identities involving inverse pairs of symbolic operators are constructed. By employing their decomposition formulas, they also present a new group of integral representations of Eulerian type for the $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function $F_{2:0;0}^{0:3;3}$ [x, y], some of which include several hypergeometric functions such as $_2F_1$, $_3F_2$, an Appell function $F_3$, and the $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ functions $F_{2:0;0}^{0:3;3}$ and $F_{1:0;1}^{0:2;3}$.

• The Pure and Applied Mathematics
• /
• v.28 no.2
• /
• pp.111-117
• /
• 2021

In this paper we aim to establish a new class of six definite double integrals in terms of gamma functions. The results are obtained with the help of some definite integrals obtained recently by Kim and Edward equality. The results established in this paper are simple, interesting, easily established and may be useful potentially.

• Kyungpook Mathematical Journal
• /
• v.57 no.3
• /
• pp.393-400
• /
• 2017

Very recently, Srivastava et al. [8] introduced an extension of the Pochhammer symbol and used it to define a generalization of the generalized hypergeometric functions. In this paper, by using the generalized Pochhammer symbol, we extend the generalized Hurwitz-Lerch Zeta function by Goyal and Laddha [6] and investigate some interesting properties which include various integral representations, Mellin transforms, differential formula and generating function. Some interesting special cases of our main results are also considered.

• Kyungpook Mathematical Journal
• /
• v.59 no.4
• /
• pp.725-734
• /
• 2019

The aim of this paper is to establish two general finite integral formulas involving the product of Galué type Struve functions and Srivastava's polynomials. The results are given in terms of generalized (Wright's) hypergeometric functions. These results are obtained with the help of finite integrals due to Oberhettinger and Lavoie-Trottier. Some interesting special cases of the main results are also considered. The results presented here are of general character and easily reducible to new and known integral formulae.

• Kyungpook Mathematical Journal
• /
• v.56 no.4
• /
• pp.1169-1177
• /
• 2016

This paper is devoted to the study of Mellin, Laplace, Euler and Whittaker transforms involving Struve function, generalized Wright function and Fox's H-function. The main results are presented in the form of four theorems. On account of the general nature of the functions involved here in, the main results obtained here yield a large number of known and new results in terms of simpler functions as their special cases. For the sake of illustration some corollaries have been recorded here as special cases of our main findings.

• East Asian mathematical journal
• /
• v.35 no.1
• /
• pp.23-30
• /
• 2019

Since Mittag-Leffler introduced the so-called Mittag-Leffler function, a number of its extensions have been investigated due mainly to their applications in a variety of research subjects. Shukla and Prajapati presented a lot of formulas involving a generalized Mittag-Leffler function in a systematic manner. Motivated mainly by Shukla and Prajapati's work, we aim to investigate a generalized multi-index Mittag-Leffler function and, among possible numerous formulas, choose to present several formulas involving this generalized multi-index Mittag-Leffler function such as a recurrence formula, derivative formula, three integral transformation formulas. The results presented here, being general, are pointed out to reduce to yield relatively simple formulas including known ones.