Series Representation of the Modified Bessel Functions

TL;DR

This paper derives new power series representations for the modified Bessel functions using fractional derivatives, providing novel summation formulas that expand the mathematical tools available for these functions.

Contribution

It introduces new summation formulas for modified Bessel functions derived via fractional derivatives, which are believed to be original contributions.

Findings

New power series representations of modified Bessel functions.

Derivation of summation formulas using fractional calculus.

Potentially useful for mathematical and engineering applications.

Abstract

Some power series representations of the modified Bessel functions (McDonald functions $K_{\alpha}$) are derived using the relatively little known formalism of fractional derivatives. The resulting summation formulae are believed to be new.