Gamma function
Function
definition | Γ:C∖{−k | k∈N}→N |
definition | Γ(z):={∫∞0 tz−1 e−t dtif Re(z)>01zΓ(z+1)else |
Discussion
Γ(z)=Π(z−1)
Theorems
n∈N∧n≠0⟹Γ(n)=(n−1)! |
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Γ(z+1)=z⋅Γ(z) |
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Γ(z)⋅Γ(1−z)=πsin(π z) |
Γ(z)⋅Γ(z+1/2)=21−2z π1/2 Γ(2z) |
Reference
Wikipedia: Gamma function