Abstract

    Open Access Review Article Article ID: AMP-5-141

    A Poisson “Half-Summation” Formula

    R Rosenfelder*

    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.  

    Keywords:

    Published on: Jun 25, 2022 Pages: 68-73

    Full Text PDF Full Text HTML DOI: 10.17352/amp.000041
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