It is sure that, after a very short fraction of a second, the first time Euler saw (despite he was one-eyed and partially blind) Gauss´s **Gamma Function Multiplication Formula**:

Euler tested the expresion with to get his corollary:

Or maybe was Gauss who generalized, **Legendre´s Gamma Duplication Formula** with Euler´s ideas, I haven´t found anything about the real history.

Anyway, if we multiply Euler´s corollary by the Gamma Formula with , and if we practice the “good habit” of multiplying things by :

Then we get:

**References:**
[1]-Xavier Gourdon and Pascal Sebah, Introduction to the Gamma Function

[2]-Gamma Function @ Wikipedia Gamma Function

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