Analogues of Euler and Poisson summation formulae
Abstract
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- October 2003
- DOI:
- 10.48550/arXiv.math/0310285
- arXiv:
- arXiv:math/0310285
- Bibcode:
- 2003math.....10285R
- Keywords:
-
- Mathematics - Number Theory
- E-Print:
- 9 pages