3 papers
math.CA2025
An affirmative answer to an open problem on Ramanujan's asymptotic formula of zero-balanced hypergeometric function
Miao-kun Wang, Zhen-hang Yang, Tie-hong Zhao
In this paper, by using recurrence method and new properties of beta function and Ramanujan -function, we prove the absolute monotonicity result for a function related to Ramanu…
math.CA2024
Some new properties of the beta function and Ramanujan R-function
Zhen-Hang Yang, Miao-Kun Wang, Tie-Hong Zhao
In this paper, the power series and hypergeometric series representations of the beta and Ramanujan functions \begin{equation*} \mathcal{B}\left( x\right) =\frac{Γ\left( x\right)^{…
math.CA2023
A lower bound for the beta function
Tiehong Zhao, Miaokun Wang
We present a new lower bound for Euler's beta function, , which states that the inequality \begin{equation*} B(x,y)>\frac{x+y}{xy}\left(1-\frac{2xy}{x+y+1}\right) \end{equa…