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## Main Question or Discussion Point

I was just curious as to how I can show the following properties of the Gamma Function, they came up in some lecture notes but were just stated?

Notation: G(z) = Gamma function

2^(z) = 2 to the power of z

I = Integral from 0 to infinity

(1) G(z)*G(1-z) = pi*cosech(pi*z)

(2) (2^(2z-1))*G(z)*G(z+(1/2)) = G(2z)*G(z/2)

Taking into consideration that the definition of G(z) = I(exp(-u)*u^(z-1)du)

Thanks

Notation: G(z) = Gamma function

2^(z) = 2 to the power of z

I = Integral from 0 to infinity

(1) G(z)*G(1-z) = pi*cosech(pi*z)

(2) (2^(2z-1))*G(z)*G(z+(1/2)) = G(2z)*G(z/2)

Taking into consideration that the definition of G(z) = I(exp(-u)*u^(z-1)du)

Thanks