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math.CA2017
An accurate approximation formula for gamma function
Zhen-Hang Yang, Jing-Feng Tian
In this paper, we present a very accurate approximation for gamma function: \begin{equation*} Γ\left( x+1\right) \thicksim \sqrt{2πx}\left( \dfrac{x}{e}\right) ^{x}\left( x\sinh \f…
math.CA2017
Two asymptotic expansions for gamma function developed by Windschitl's formula
Zhen-Hang Yang, Jing-Feng Tian
In this paper, we develop Windschitl's approximation formula for the gamma function to two asymptotic expansions by using a little known power series. In particular, for $n\in \mat…
math.CA2017★ 11 cited
Convexity and monotonicity for the elliptic integrals of the first kind and applications
Zhen-Hang Yang, Jingfeng Tian
The elliptic integral and its various generalizations are playing very important and basic role in different branches of modern mathematics. It is well known that they cannot be re…