A Poisson "Half-Summation" Formula
<p>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 exponentia...
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| Format: | Book |
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Annals of Mathematics and Physics - Peertechz Publications,
2022-06-25.
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| Summary: | <p>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. </p> |
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| DOI: | 10.17352/amp.000041 |