Generalization of some of Ramanujan's formulae

Aung Phone Maw

Generalization of some of Ramanujan's formulae

General Mathematics 2025-01-17 v5

Authors: Aung Phone Maw

Abstract

We shall make use of the method of partial fractions to generalize some of Ramanujan's infinite series identities, including Ramanujan's famous formula for $\zeta(2n+1)$ , and we shall also give a generalization of the transformation formula for the Dedekind eta function. It is shown here that the method of partial fractions can be used to obtain many similar identities of this kind.

Keywords

Ramanujan's formulae partial fractions infinite series zeta function Dedekind eta function

Cite

@article{arxiv.2408.09077,
  title  = {Generalization of some of Ramanujan's formulae},
  author = {Aung Phone Maw},
  journal= {arXiv preprint arXiv:2408.09077},
  year   = {2025}
}

Comments

16 pages, feedback are welcomed

Related papers

View all related →