arXiv:2610.40730v1 Announce Type: new Abstract: We consider special cases of the discontinuous Weber--Schafheitlin integral in which the orders $\mu$ and $\nu$ of the Bessel functions differ by an integer and the exponent $\lambda$ equals $0$ or $\pm1$, with $\mu-\nu+\lambda$ odd. Explicit closed-form results are obtained in terms of Jacobi polynomials.
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