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On Infinite Series of Bessel functions of the First Kind: $\sum_ν J_{Nν+p}(x), \sum_ν(-1)^νJ_{Nν+p}(x)$
Published 1 Nov 2022 in math-ph, math.CA, and math.MP | (2211.01148v1)
Abstract: Infinite series of Bessel function of the first kind, $\sum_\nu{\pm\infty} J_{N\nu+p}(x)$, $\sum_\nu{\pm\infty} (-1)\nu J_{N\nu+p}(x)$, are summed in closed form. These expressions are evaluated by engineering a Dirac comb that selects specific sequences within the Bessel series.
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