Analogues of Euler and Poisson summation formulae

Details Analogues of Euler and Poisson summation formulae Analogues of Euler and Poisson summation formulae

2003-10-18

arxiv.org/abs/math/0310285v1

Proc. Indian Acad. Sci. (Math. Sci.), Vol. 113, No. 3, August 2003, pp. 213-221

Mathematics

Number Theory

9 pages

Scientific paper

Euler--Maclaurin and Poisson analogues of the summations $\sum_{a < n \leq b} \chi(n) f(n)$, $\sum_{a < n \leq b} d(n) f(n)$, $\sum_{a < n \leq b} d(n) \chi (n) f(n)$ have been obtained in a unified manner, where $(\chi (n))$ 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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