• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1239-1248
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• 2018

Recently, many authors have obtained several hypergeometric identities involving hypergeometric functions of one and multi-variables such as the Appell's functions and Horn's functions. In this paper, we obtain several new transformations suitably by applying the fractional calculus operator to these hypergeometric identities, which was introduced recently by Tremblay.

• The Pure and Applied Mathematics
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• v.20 no.4
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• pp.233-242
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• 2013

Certain interesting single (or double) infinite series associated with hypergeometric functions have been expressed in terms of Psi (or Digamma) function ${\psi}(z)$, for example, see Nishimoto and Srivastava [8], Srivastava and Nishimoto [13], Saxena [10], and Chen and Srivastava [5], and so on. In this sequel, with a view to unifying and extending those earlier results, we first establish two relations which some double infinite series involving hypergeometric functions are expressed in a single infinite series involving ${\psi}(z)$. With the help of those series relations we derived, we next present two functional relations which some double infinite series involving $\bar{H}$-functions, which are defined by a generalized Mellin-Barnes type of contour integral, are expressed in a single infinite series involving ${\psi}(z)$. The results obtained here are of general character and only two of their special cases, among numerous ones, are pointed out to reduce to some known results.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.465-471
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• 2016

In this paper, we establish certain integrals involving Srivastava's Polynomials [5] and Aleph Function ([8], [10]). On account of general nature of the functions and polynomials involved in the integrals, our results provide interesting unifications and generalizations of a large number of new and known results, which may find useful applications in the field of science and engineering. To illustrate, we have recorded some special cases of our main results which are also sufficiently general and unified in nature and are of interest in themselves.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.341-345
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• 2007

In this paper we show that the second order mock theta function, given by Hikami, is bounded and satisfies the second condition for the mock theta functions.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.211-220
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• 2005

In this paper we obtain the transformations of the Ramanujan's tenth order mock theta functions under the modular group generators ${\tau}\;{\rightarrow}\;{\tau}\;+\;1\;and\;{\tau}\;{\rightarrow}\;-1/ {\tau}\;where\;q\;=\;e^{{\pi}it}$.

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.165-175
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• 2010

In the paper we consider deemed three mock theta functions introduced by Hikami. We have given their alternative expressions in double summation analogous to Hecke type expansion. In proving we also give a new Bailey pair relative to $a^2$. I presume they will be helpful in getting fundamental transformations.

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

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.101-116
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• 1985

• Kyungpook Mathematical Journal
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• v.22 no.1
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• pp.103-107
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• 1982

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.473-506
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• 2016

This paper continues the study of recursion formulas of multivariable hypergeometric functions. Earlier, in [4], the authors have given the recursion formulas for three variable Lauricella functions, Srivastava's triple hypergeometric functions and k-variable Lauricella functions. Further, in [5], we have obtained recursion formulas for the general triple hypergeometric function. We present here the recursion formulas for Exton's triple hypergeometric functions.