The evaluation of single Bessel function sums

R. B. Paris

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    We examine convergent representations for the sums of Bessel functions X∞ n=1 Jν(nx) nα (x > 0) and X∞ n=1 Kν(nz) nα (<(z) > 0), together with their alternating versions, by a Mellin transform approach. We take α to be a real parameter with ν > − 1 2 for the first sum and ν ≥ 0 for the second sum. Such representations enable easy computation of the series in the limit x or z → 0+. Particular attention is given to logarithmic cases that occur for certain values of α and ν
    Original languageEnglish
    Pages (from-to)71-82
    Number of pages12
    JournalMathematica Æterna
    Issue number2
    Publication statusPublished - 2018


    • Bessel functions
    • Schlomilch-type series
    • Mellin transform


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