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Errors and ambiguity in transition from Fourier series to Fourier integrals

2004/12/13 by В. К. Петров, Vladimir K. Petrov, Petrov, Vladimir K.
Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Mathematical functions and polynomials #Numerical methods for differential equations #hep-lat

paper · pdf · doi:10.48550/arxiv.hep-lat/0412019

arxiv created 2004/12/13 · openalex publication_date 2004/12/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Transition from Fourier series to Fourier integrals is considered and error introduced by ordinary substitution of integration for summing is estimated. Ambiguity caused by transition from discrete function to continuous one is examined and conditions under which this ambiguity does not arise are suggested.

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