Generalization of Ramanujan's Continued Fractions for Even Order

Dipika Sarkar; S. N. Fathima; M. P. Thejitha

Generalization of Ramanujan's Continued Fractions for Even Order

Number Theory 2026-07-15 v1

Authors: Dipika Sarkar , S. N. Fathima , M. P. Thejitha

Abstract

In this paper, we derive three generalized continued fractions of any even order $k$ with the aid of a general continued fraction identity of Ramanujan and we establish general theta function identities for these continued fractions. As an application of continued fraction of order seventy-six, we obtain partition theoretic identities and some vanishing coefficient results.

Keywords

Ramanujan's continued fractions theta function identities partition identities vanishing coefficients even order

Cite

@article{arxiv.2607.13600,
  title  = {Generalization of Ramanujan's Continued Fractions for Even Order},
  author = {Dipika Sarkar and S. N. Fathima and M. P. Thejitha},
  journal= {arXiv preprint arXiv:2607.13600},
  year   = {2026}
}