A Poisson "Half-Summation" Formula

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R Rosenfelder*

Abstract

A generalization of Poisson’s summation formula is derived – in a non-rigorous way – allowing evaluation of sums from 1 (or any finite integer) ¥ instead of the usual range -¥+¥. This is achieved in two ways, either by introducing a converging factor in a geometric series of exponential functions and letting it approach zero in a controlled way or by applying a Hilbert transform to the series. Several examples illustrate its usefulness in the evaluation of series and specific applications.

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Rosenfelder, R. (2022). A Poisson "Half-Summation" Formula. Annals of Mathematics and Physics, 5(1), 068–073. https://doi.org/10.17352/amp.000041
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Copyright (c) 2022 Rosenfelder R.

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