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Analogues of Euler and Poisson summation formulae

Vivek V Rane
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Abstract

Euler--Maclaurin and Poisson analogues of the summations $\sum_{a < n \leq b} χ(n) f(n)$, $\sum_{a < n \leq b} d(n) f(n)$, $\sum_{a < n \leq b} d(n) χ(n) f(n)$ have been obtained in a unified manner, where $(χ(n))$ is a periodic complex sequence; $d(n)$ is the divisor function and $f(x)$ 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.

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Vivek V Rane. 2003-10-18. Analogues of Euler and Poisson summation formulae. https://arxiv.org/abs/math/0310285

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