Let's introduce an interesting identity.
especially, if , it turns to
Proof:
From the known Weierstrass Expansion of Gamma Function, we have
Timing by two sides of formula , and noticing that , we get
Replacing by in identity while let be a substitute of in identity where , we obtain
Multiplying and with the increase of from to , we finally simplify to
Peculiarly, when , there is
As for this question, note that