CERTAIN FRACTIONAL INTEGRALS OF GENERALIZED BESSEL FUNCTIONS OF THE FIRST KIND

Recently, Choi and Agarwal [1] gave two integral formulas whose integrands are the integrand given in the Oberhettinger’s integral formula [2] and the Bessel function of the first kind. Motivated essentially by this work [1], we aim at presenting two very general integral formulas whose integrands are the integrand given in the Oberhettinger’s integral formula [2] and a finite product of the generalized Bessel function of the first kind, which are expressed in terms of the generalized Lauricella functions. Among a large number of interesting and potentially useful special cases of our main results, only 8 integral formulas involving such elementary functions as trigonometric and hyperbolic functions are also considered.