Open Access Research

Certain unified integrals associated with Bessel functions

Junesang Choi1* and Praveen Agarwal2

Author affiliations

1 Department of Mathematics, Dongguk University, Gyeongju, Korea

2 Department of Mathematics, Anand International College of Engineering, Jaipur, 303012, India

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Citation and License

Boundary Value Problems 2013, 2013:95  doi:10.1186/1687-2770-2013-95

Published: 18 April 2013

Abstract

A remarkably large number of integral formulas involving a variety of special functions have been developed by many authors. Very recently, Ali gave three interesting unified integrals involving the hypergeometric function <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/95/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/95/mathml/M3">View MathML</a>. Using Ali’s method, in this paper, we present two generalized integral formulas involving the Bessel function of the first kind <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/95/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/95/mathml/M2">View MathML</a>, which are expressed in terms of the generalized (Wright) hypergeometric functions. Some interesting special cases of our main results are also considered.

MSC: 33B20, 33C20, 33B15, 33C05.

Keywords:
Gamma function; hypergeometric function <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/95/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/95/mathml/M3">View MathML</a>; generalized hypergeometric function <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/95/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/95/mathml/M4">View MathML</a>; generalized (Wright) hypergeometric functions <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/95/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/95/mathml/M5">View MathML</a>; Bessel function of the first kind; Oberhettinger’s integral formula; Garg and Mittal’s integral formula