Integral representations and asymptotic expansions for the second type Neumann series of Bessel functions of the first kind

Álvaro Romaniega

In this paper we study the following Bessel series ${\sum }_{l=1}^{\infty }{J}_{l+m^{\prime }}(r)J_{l+m}(r)(l+\beta {)}^{\alpha }$ for any $m,m^{\prime }\in \mathbb{Z}$, $\alpha \in \mathbb{R}$ and $\beta >-1$. They are a par…