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Gamma function

Function

definition Γ:C{k | kN}N
definition Γ(z):={0  tz1 et dtif Re(z)>01zΓ(z+1)else

Discussion

Γ(z)=Π(z1)

Theorems

nNn0Γ(n)=(n1)!
Γ(z+1)=zΓ(z)
Γ(z)Γ(1z)=πsin(π z)
Γ(z)Γ(z+1/2)=212z π1/2 Γ(2z)

Reference

Wikipedia: Gamma function


Context

Equivalent to

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