Integral representations for Neumann-type series of Bessel functions $I_\nu ,$ $Y_\nu$ and $K_\nu$

Abstract:

Recently Pogány and Süli [Proc. Amer. Math. Soc. 137(7) (2009), 2363–2368] derived a closed-form integral expression for Neumann series of Bessel functions of the first kind $J_\nu$. In this paper our aim is to establish analogous integral representations for the Neumann-type series of modified Bessel functions of the first kind $I_\nu$ and for Bessel functions of the second kind $Y_\nu , K_\nu$, and to give links for the same question for the Hankel functions $H_\nu ^{(1)}, H_\nu ^{(2)}$.