Commun. Korean Math. Soc. 2019; 34(2): 523-532
Online first article November 16, 2018 Printed April 30, 2019
https://doi.org/10.4134/CKMS.c180147
Copyright © The Korean Mathematical Society.
Yongsup Kim
Wonkwang University
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.
Keywords: Gamma function, generalized hypergeometric function ${}_pF_q$, generalized (Wright) hypergeometric functions ${}_p\Psi_q$, generalized Lauricella series in several variables, generalized $k$-Bessel function of the first kind, Oberhettinger's integral form
MSC numbers: Primary 33B20, 33C20; Secondary 33B15, 33C05
2013; 28(2): 297-301
2020; 35(1): 63-81
2017; 32(4): 909-914
2017; 32(1): 47-53
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd