On Some Special Cases of the Weber-Schafheitlin Integral

Abstract

We consider special cases of the discontinuous Weber--Schafheitlin integral in which the orders $μ$ and $ν$ of the Bessel functions differ by an integer and the exponent $λ$ equals $0$ or $\pm1$, with $μ-ν+λ$ odd. Explicit closed-form results are obtained in terms of Jacobi polynomials.