Generalzed Bessel Recursion Relations

TL;DR

This paper introduces generalized recursion relations for Bessel functions, extending the classic three-term formulas to sums with arbitrary numbers of terms, providing a broader framework for their recursive properties.

Contribution

It presents a new class of finite sum identities for Bessel functions that generalize existing three-term recursion formulas.

Findings

Finite sum identities for Bessel functions established.

Reduction to classical three-term recursion in simple cases.

Potential applications in mathematical analysis and physics.

Abstract

This paper presents the equality of finite index sums of Bessel func- tions containing arbitrary numbers of terms. These reduce to the familiar three term recursion formulas in simple cases.