Certain integration formulae for the generalized $k$-Bessel functions and Deleure hyper-Bessel function
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Integrals involving a finite product of the generalized Bessel functions have recently been studied by Choi {\it et al.}~\cite{Ch-Ag, Ch-Ku-Pu}. Motivated by these results, we establish certain unified integral formulas involving a finite product of the generalized $k$-Bessel functions. Also, we consider some integral formulas of the $(p, q)$-extended Bessel functions $J_{\nu,p,q}(z)$ and the Delerue hyper-Bessel function which are proved in terms of $(p, q)$-extended generalized hypergeometric functions, and the generalized Wri\-ght hypergeometric functions, respectively.
Abstract
Integrals involving a finite product of the generalized Bessel functions have recently been studied by Choi {\it et al.}~\cite{Ch-Ag, Ch-Ku-Pu}. Motivated by these results, we establish certain unified integral formulas involving a finite product of the generalized $k$-Bessel functions. Also, we consider some integral formulas of the $(p, q)$-extended Bessel functions $J_{\nu,p,q}(z)$ and the Delerue hyper-Bessel function which are proved in terms of $(p, q)$-extended generalized hypergeometric functions, and the generalized Wri\-ght hypergeometric functions, respectively.
참고문헌 (14)
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