English

An affirmative answer to an open problem on Ramanujan's asymptotic formula of zero-balanced hypergeometric function

Classical Analysis and ODEs 2025-04-08 v1

Abstract

In this paper, by using recurrence method and new properties of beta function and Ramanujan RR-function, we prove the absolute monotonicity result for a function related to Ramanujan asymptotic formula of zero-balanced hypergeometric function, which gives an affirmative answer to an open problem proposed by Anderson Vamanamurthy and Vuorinen \cite{Anderson-CIIQM-JW-1997} in 1997.

Cite

@article{arxiv.2504.04521,
  title  = {An affirmative answer to an open problem on Ramanujan's asymptotic formula of zero-balanced hypergeometric function},
  author = {Miao-kun Wang and Zhen-hang Yang and Tie-hong Zhao},
  journal= {arXiv preprint arXiv:2504.04521},
  year   = {2025}
}

Comments

19 pages

R2 v1 2026-06-28T22:48:37.764Z