A continued product approximation for the gamma function

作者：Feng Lei; Wang Weiping^*

来源：Integral Transforms and Special Functions, 2013, 24(10): 831-839.

DOI：10.1080/10652469.2012.762710

• approximations
• gamma function
• Stirling's formula

In this paper, we establish a continued product approximation for the gamma function:
Gamma(x+1) similar to root 2 pi e.e(-a) (x+1+a/e)(x+3/2) 1/x+1 Pi(n)(i=1) (1 + 1/x(i) )(gamma i) ,
where the powers (i) can be determined by a recurrence. It can be seen that one of Mortici's [A class of integral approximations for the factorial function. Comput. Math. Appl. 2010;59(6):2053-2058] results is a special case of our approximation and can be viewed as the zeroth truncation. Some numerical computations are also made to show the performance of this formula.

• 出版日期2013-10-1
• 单位浙江理工大学