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5.9.13  The Γ function: Gamma

Gamma takes as argument a number a.
Gamma returns the value of the Γ function in a, defined by:

Γ(x)=
+∞


0
ettx−1dt,  if  x>0 

If x is a positive integer, Γ is computed by applying the recurrence:

Γ(x+1)=x*Γ(x),    Γ(1)=1 

Hence:

Γ(n+1)=n

Input:

Gamma(5)

Output:

24

Input:

Gamma(0.7)

Output:

1.29805533265

Input:

Gamma(-0.3)

Output:

-4.32685110883

Indeed: Gamma(0.7)=-0.3*Gamma(-0.3)
Input:

Gamma(-1.3)

Output:

3.32834700679

Indeed Gamma(0.7)=-0.3*Gamma(-0.3)=(-0.3)*(-1.3)*Gamma(-1.3)


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