• 호남수학학술지
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• 제16권1호
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• pp.47-54
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• 1994

We present a generating function and three semi-orthogonal relations for a class of hypergeometric functions. We employ semi-orthogonal relations to generate a theory concerning finite series expansions involving our hypergeometric functions.

• 호남수학학술지
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• 제39권3호
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• pp.443-451
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• 2017

Very recently, Agarwal gave remakably a scads of fractional integral formulas involving various special functions. Using the same technique, we obtain certain(presumably) new fractional integral formulas involving the product of confluent hypergeometric functions. Some interesting special cases of our two main results are considered.

• 대한수학회논문집
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• 제28권3호
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• pp.527-534
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• 2013

We first aim at proving an interesting easily derivable summation formula. Then it is easily seen that this formula immediately yields a hypergeometric summation theorem recently added to the literature by Qureshi et al. Moreover we apply the main formulas to present some interesting summation formulas, whose special cases are also seen to yield the earlier known results.

• East Asian mathematical journal
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• 제21권2호
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• pp.191-203
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• 2005

In the present paper we first establish some basic results for a substantially more general class of functions defined below. The results include simple differentiation and fractional calculus operators(integration and differentiation of arbitrary orders) for this class of functions. These results are then invoked in determining similar properties for the generalized Wright's hypergeometric functions. Further, norm estimate of a certain class of integral operators whose kernel involves the generalized Wright's hypergeometric function, and its composition(and other related properties) with the fractional calculus operators are also investigated.

• 대한수학회논문집
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• 제28권2호
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• pp.297-301
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• 2013

When certain general single or multiple hypergeometric functions were introduced, their reduction formulas have naturally been investigated. Here, in this paper, we aim at presenting a very interesting reduction formula for the Srivastava's triple hypergeometric function $F^{(3)}[x,y,z]$ by applying the so-called Beta integral method to the Henrici's triple product formula for hypergeometric series.

• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.781-795
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• 2020

In this paper, we obtain an analytical solution for an unsolved definite integral RC (m, n) from a 1915 paper of Srinivasa Ramanujan. We obtain our solution using the hypergeometric approach and an infinite series decomposition identity. Also, we give some generalizations of Ramanujan's integral RC (m, n) defined in terms of the ordinary hypergeometric function 2F3 with suitable convergence conditions. Moreover as applications of our result we obtain nine new infinite summation formulas associated with the hypergeometric functions 0F1, 1F2 and 2F3.

• 대한수학회논문집
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• 제32권1호
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• pp.47-53
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• 2017

Generalized integral formulas involving the generalized modified k-Bessel function $J^{b,c,{\gamma},{\lambda}}_{k,{\upsilon}}(z)$ of first kind are expressed in terms generalized Wright functions. Some interesting special cases of the main results are also discussed.

• 대한수학회논문집
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• 제34권2호
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• pp.507-522
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• 2019

The main aim of this present paper is to present a new extension of the fractional derivative operator by using the extension of beta function recently defined by Shadab et al. [19]. Moreover, we establish some results related to the newly defined modified fractional derivative operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

• 호남수학학술지
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• 제33권4호
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• pp.441-452
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• 2011

The enormous success of the theory of hypergeometric series in a single variable has stimulated the development of a corresponding theory in two and more variables. A wide variety of investigations in the theory of several variable hypergeometric functions have been essentially motivated by the fact that solutions of many applied problems involving partial differential equations are obtainable with the help of such hypergeometric functions. Here, in this trend, we aim at presenting further decomposition formulas for Saran function $F_E$, which are used to give some integral representations of the function $F_E$. We also present a system of partial differential equations for the Saran function $F_E$.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.439-447
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• 2015

Very recently the authors have obtained a very interesting reduction formula for the Srivastava's triple hypergeometric series $F^{(3)}$(x, y, z) by applying the so-called Beta integral method to the Henrici's triple product formula for the hypergeometric series. In this sequel, we also present three more interesting reduction formulas for the function $F^{(3)}$(x, y, z) by using the well known identities due to Bailey and Ramanujan. The results established here are simple, easily derived and (potentially) useful.