Weber-Schafheitlin integrals with arbitrary exponent

TL;DR

This paper derives explicit formulas for Weber-Schafheitlin integrals with arbitrary exponents, interpreting them as kernels of operators linked to the Aharonov-Bohm Hamiltonian, including cases where the exponent is ≥ 1.

Contribution

It provides new explicit formulas for Weber-Schafheitlin integrals with arbitrary exponents, including distributional cases, and connects them to quantum mechanical operators.

Findings

Explicit formulas for Weber-Schafheitlin integrals with exponent ≥ 1.

Interpretation of these integrals as kernels of physically relevant operators.

Discussion of special cases and distributional aspects.

Abstract

We present explicit formulae for Weber-Schafheitlin type integrals and give them an interpretation as the kernel of a physically relevant operator related to the hamiltonian of Aharanov and Bohm. In particular, we derive explicit formulae for Weber-Schafheitlin type integrals with exponent larger or equal 1, which are distributions on R_+. We discuss several special cases.