初一牲,学了一点高数,想了半天没想出来
求证: Γ(s)=1s∏n=1∞{(1+sn)−1(1+1n)s}\Gamma (s)=\frac{1}{s}\prod\limits_{n=1}^{\infty}\left\{\left(1+\frac{s}{n}\right)^{-1}\left(1+\frac{1}{n}\right)^{s}\right\}Γ(s)=s1n=1∏∞{(1+ns)−1(1+n1)s}
Γ\GammaΓ原函数:
Γ(s)=∫0+∞e−xxs−1 dx\Gamma (s)=\int^{+\infty}_{0}e^{-x}x^{s-1}\,dxΓ(s)=∫0+∞e−xxs−1dx