Analogues of Euler and Poisson summation formulae
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.
Volume 132, 2022
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