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

2025/04/06 by Wang, Miao-kun, Yang, Zhen-hang, Zhao, Tie-hong
#26A48 #33C05 #40A05 #41A10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.04521

Abstract

In this paper, by using recurrence method and new properties of beta function and Ramanujan R-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 \citeAnderson-CIIQM-JW-1997 in 1997.

Related

• Some new properties of the beta function and Ramanujan R-function
• Ramanujan's cubic transformation inequalities for zero-balanced hypergeometric functions
• Remark On Two Results due to Ramanujan on Hypergeometric Series
• Reflections on Ramanujan's Mathematical Gems
• Contributions to the theory of Ramanujan's function τ(n) and similar arithmetical functions