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    • Analogues of Euler and Poisson summation formulae

      Vivek V Rane

      Volume 113 Issue 3 August 2003 pp 213-221

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/113/03/0213-0221

    • Keywords

       

      Abel’s summation formula; Euler summation formula; Euler-Maclaurin summation formula; Poisson’s summation formula; Fourier series

    • Abstract

       

      Euler-Maclaurin and Poisson analogues of the summations εa <n ≤b χ(n)f(n), have been obtained in a unified manner, where (χ(n)) is a periodic complex sequence;d(n) is the divisor function andf(x) is a sufficiently smooth function on [a, b]. We also state a generalised Abel’s summation formula, generalised Euler’s summation formula and Euler’s summation formula in several variables.

    • Author Affiliations

       

      Vivek V Rane1

      1. Department of Mathematics, The Institute of Science, 15, Madam Cama Road, Mumbai - 400 032, India

    • Dates

       
      Published
      August 2003
      Manuscript received
      2 February 2002
      Manuscript revised
      20 January 2003

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