Expansion of Infinite Series Containing Modified Bessel Functions of the Second Kind

TL;DR

This paper develops a method to derive asymptotic expansions for infinite series involving modified Bessel functions of the second kind, with applications in quantum field theory.

Contribution

It introduces a novel approach for constructing asymptotic expansions of series with Bessel functions when one parameter is small, applicable to quantum field theory problems.

Findings

Derived a new asymptotic expansion method for Bessel series

Validated the method with quantum field theory applications

Provided explicit formulas for specific series cases

Abstract

The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the parameters in the argument of the modified Bessel function of the second kind is small compared to the others. We apply the results obtained for the asymptotic expansion to specific problems that arise in the ambit of quantum field theory.