Wallis公式与Stirling公式的推广

数学理论与应用 ›› 2017, Vol. 37 ›› Issue (2): 73-78.

Wallis公式与Stirling公式的推广

韩凯

国防科技大学光电科学与工程学院,湖南长沙,410073

出版日期:2017-06-30 发布日期:2020-09-23

Extension of the Wallis Formula and Stirling Formula

Han Kai

College of Opto-Electronic Science and Engineering National University of Defense Technology,Changsha 410073,China

Online:2017-06-30 Published:2020-09-23

摘要/Abstract

摘要：

Wallis公式和Stirling公式是高等数学中两个重要的公式.本文将Wallis公式和Stirling公式中的通项序数n推广为实数n+a,得到广义Wallis公式和广义Stirling公式,并讨论二者之间的内在联系.

关键词: Wallis公式, Stirling公式, 伽马函数Γ(x), 贝塔函数B(p,q)

Abstract: Wallis’formula and Stirling’s formula are two important formulas in advanced mathematics.In this paper we firstly extend these formulas to non-integer situation to yield a generic Wallis formula and a generic Stirling formula, and then investigate the relation between these formulas.

Key words: Wallis＇formula, Stirling＇s formula, FunctionΓ(x), Function B(p,q)

韩凯. Wallis公式与Stirling公式的推广[J]. 数学理论与应用, 2017, 37(2): 73-78.

Han Kai.

Extension of the Wallis Formula and Stirling Formula [J]. Mathematical Theory and Applications, 2017, 37(2): 73-78.