A Generalisation of Ramanujan's (back of the envelope) Method for Divergent Series
Number Theory
2023-03-27 v1 Combinatorics
Abstract
Ramanujan derived the well known divergent-sum of integers in more than one way. We generalise the informal method to higher powers of the Riemann zeta function through a study of the Eulerian numbers in particular. Within the context of additive combinatorics a heuristic approach that unifies generating series and difference matrices is presented.
Keywords
Cite
@article{arxiv.2303.14045,
title = {A Generalisation of Ramanujan's (back of the envelope) Method for Divergent Series},
author = {Patrick J. Burchell},
journal= {arXiv preprint arXiv:2303.14045},
year = {2023}
}
Comments
13 pages, 1 figure