CERTAIN INTEGRALS INVOLVING 2F1, KAMPÉDE FÉRIET FUNCTION AND SRIVASTAVA POLYNOMIALS

Title & Authors
CERTAIN INTEGRALS INVOLVING 2F1, KAMPÉDE FÉRIET FUNCTION AND SRIVASTAVA POLYNOMIALS
Agarwal, Praveen; Chand, Mehar; Choi, Junesang;

Abstract
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 $\small{_2F_1}$, Srivastava polynomials, and $\small{Kamp{\acute{e}}}$ de $\small{F{\acute{e}}riet}$ 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.
Keywords
hypergeometric functions;$\small{Kamp{\acute{e}}}$ de $\small{F{\acute{e}}riet}$ function;Srivastava polynomials;Hermite polynomials;Laguerre polynomials;
Language
English
Cited by
References
1.
P. Agarwal, On a new theorem involving the generalized Mellin-Barnes type of contour integrals and Srivastava polynomials, J. Appl. Math. Stat. Inform. 8 (2012), no. 2, 29-35.

2.
P. Agarwal and M. Chand, New theorems involving the generalized Mellin-Barnes type of contour integrals and general class of polynomials, Glob. J. Sci. Frontier Res. Math. Decision Sci. 12 (2012), no. 3, 15-24.

3.
M. Chand, New theorems involving the I-function and general class of polynomials, Glob. J. Sci. Frontier Res. Math. Decision Sci. 12 (2012), no. 4, 89-99.

4.
M. I. Qureshi, K. A. Quraishi, and R. Pal, Some definite integrals of Gradshteyn-Ryzhik and other integrals, Glob. J. Sci. Frontier Res. Math. Decision Sci. 11 (2011), no. 4, 75-80.

5.
L. J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, 1966.

6.
I. N. Sneddon, The Use of Integral Transforms, Tata McGraw-Hill, New Delhi, 1979.

7.
H. M. Srivastava, A contour integral involving Fox's H-function, Indian J. Math. 14 (1972), 1-6.

8.
H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985.

9.
H. M. Srivastava and R. Panda, Some bilateral generating functions for a class of generalized hypergeometric polynomials, J. Reine Angew. Math. 283/284 (1976), 265-274.

10.
H. M. Srivastava and N. P. Singh, The integration of certain products of the multivariable H-function with a general class of polynomials, Rend. Circ. Mat. Palermo 32 (1983), no. 2, 157-187.

11.
G. Szego, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ. 23, Fourth edi., Amer. Math. Soc. Providence, Rhode Island, 1975.

12.
E. M. Wright, The asymptotic expansion of the generalized Bessel function, Proc. London Math. Soc. (2) 38 (1935), 257-260.