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

Recently Pog\'any and S\"uli [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 note our aim is to establish analogous integral representations for the Neumann-type series of modified Bessel functions of the first kind $I_\nu$, for Bessel functions of the second kind $Y_\nu, K_\nu$ and to give links for the same question for the Hankel functions $H_\nu^(1) ; H_\nu^(2)$.

Bessel and modified Bessel functions of the first and the second kind; Neumann series of Bessel and modified Bessel functions of first and second kind

nije evidentirano