• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.679-689
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• 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 $F_{1:0;1}^{0:2;3}$.

• Honam Mathematical Journal
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• v.33 no.1
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• pp.43-50
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• 2011

The aim of this paper is to obtain twenty five Eulerian type double integrals in the form of a general double integral involving Kamp$\'{e}$ de F$\'{e}$riet function. The results are derived with the help of the generalized classical Watson's theorem obtained earlier by Lavoie, Grondin and Rathie. A few interesting special cases of our main result are also given.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.205-212
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• 2011

The aim of this paper is to obtain twenty five Eulerian type single integrals in the form of a general single integral involving $Kamp\acute{e}$ de $F\acute{e}riet$ function. The results are derived with the help of the generalized classical Watson's theorem obtained earlier by Lavoie, Grondin and Rathie. A few interesting special cases of our main result are also given.

• Honam Mathematical Journal
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• v.31 no.2
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• pp.167-176
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• 2009

The aim of this paper is to obtain three interesting results for reducibility of Kamp$\'{e}$ de $\'{e}$riet function. The results are derived with the help of contiguous Gauss's second summation formulas obtained earlier by Lavoie et al. The results obtained by Bailey, Rathie and Nagar follow special cases of our main findings.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.187-204
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• 2011

B. C. Carlson [Some extensions of Lardner's relations between $_0F_3$ and Bessel functions, SIAM J. Math. Anal. 1(2) (1970), 232-242] presented several useful relations between Bessel and generalized hypergeometric functions that generalize some earlier results. Here, by simply splitting Srivastava's hypergeometric function $H_B$ into eight parts, we show how some useful and generalized relations between Srivastava's hypergeometric functions $H_B$ and $F^{(3)}$ can be obtained. These main results are shown to be specialized to yield certain relations between functions $_0F_1$, $_1F_1$, $_0F_3$, ${\Psi}_2$, and their products including different combinations with different values of parameters and signs of variables. We also consider some other interesting relations between the Humbert ${\Psi}_2$ function and $Kamp\acute{e}$ de $F\acute{e}riet$ function, and between the product of exponential and Bessel functions with $Kamp\acute{e}$ de $F\acute{e}riet$ functions.

• Honam Mathematical Journal
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• v.36 no.2
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• pp.345-355
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• 2014

The main objective of this paper is to obtain a formula containing eleven interesting results for the reducibility of Kamp$\acute{e}$ de F$\acute{e}$riet function. The results are derived with the help of two general results for the series $_2F_1(2)$ very recently presented by Kim et al. Well known Kummer's second theorem and its contiguous results proved earlier by Rathie and Nagar, and Kim et al. follow special cases of our main findings.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.397-409
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• 2018

The aim of this research note is to evaluate two generalized integrals involving the product of generalized Bessel function and Jacobi polynomial by employing the result of Obhettinger [2]. Also, by mean of the main results, we have established an interesting relation in between $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ and Srivastava and Daoust functions. Some interesting special cases of our main results are also indicated.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.343-353
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• 2016

A remarkably large number of integrals whose integrands are associated, in particular, with a variety of special functions, for example, the hypergeometric and generalized hypergeometric functions have been recorded. Here we aim at presenting certain (presumably) new and (potentially) useful integral formulas whose integrands are involved in a product of $_2F_1$, Srivastava polynomials, and $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ functions. The main results are derived with the help of some known definite integrals obtained earlier by Qureshi et al. [4]. Some interesting special cases of our main results are also considered.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.63-101
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• 2021

In this research paper, an attempt has been made to provide an interesting extension of the well-known and useful Kummer's second theorem. Several applications have also been given.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.611-622
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• 2011

The present paper deals with generalization of several families of bilinear and bilateral generating functions for the heat type polynomials suggested by Jacobi polynomials with different argument.