arXiv subjects
Publications and source records attributed to Miaokun Wang.
We present a new lower bound for Euler's beta function, $B(x,y)$, which states that the inequality \begin{equation*} B(x,y)>\frac{x+y}{xy}\left(1-\frac{2xy}{x+y+1}\right) \end{equation*} holds on $(0,1]\times(0,1]$, which improves a lower bound obtained by P. Ivády [12, Theorem, (3.2)] in the case of $0<x+y<1$.
We study the quotient of hypergeometric functions \begin{equation*} μ_{a}^*(r)=\fracπ{2\sin{(πa)}}\frac{F(a,1-a;1;1-r^3)}{F(a,1-a;1;r^3)} \quad (r\in(0,1)) \end{equation*} in the theory of Ramanujan's generalized modular equation for $a\in(0,1/2]$, find an infinite product formula for $μ_{1/3}^*(r)$ by use of the properties of $μ_{a}^*(r)$ and Ramanujan's cubic transformation. Besides, a new cubic transformation formula of hypergeometric function is given, which complements the Ramanujan's cubic transformation.