A Summation of Series Involving Bessel Functions and Order Derivatives of Bessel Functions

Abstract

In this note, we derive the closed-form expression for the summation of series ${\sum }_{n=0}^{\infty }n{J}_n(x)\partial J_n/\partial n$, which is found in the calculation of entanglement entropy in 2-d bosonic free field, in terms of $Y_0$, $J_0$ and an integral involving these two Bessel functions. Further, we point out the integral can be expressed as a Meijer G function.

Cited by in corpus (1)

• Sums of products of Bessel functions and order derivatives of Bessel functions