Proofs Related to the Gamma Function

In this video, I go over proofs of many of the formulas mentioned in my last video outlining the Gamma function, an extension of the factorial to the real and complex numbers.

I did not cover the proofs of the Hankel form or the Multiplication Theorem as they are used a little less compared to the other formulas, but you can try proving them yourself or I might possibly cover them in a future video.

Last video has more context for the formulas if you didn't watch it first:    • Extending the Factorial with the Gamma Fun...  

Timecodes:
0:00 - Stirling's Approximation
5:35 - Beta-Gamma Relationship
11:49 - Euler Representation of Γ(z)
17:50 - Weierstrass Representation of Γ(z)
25:07 - Reflection Formula
29:57 - Duplication Formula

Sources and other tidbits:
Gamma Function Outline: https://en.wikipedia.org/wiki/Gamma_f...
More on the Beta Function: https://en.wikipedia.org/wiki/Beta_fu...
Gamma Function as Area Under a Curve in Desmos: https://www.desmos.com/calculator/e4z...

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