The Gamma function is defined by
Γ(x)= | ∫ |
| e−ttx−1dt, if x>0. |
If x is a positive integer, Γ is computed by applying the recurrence Γ(x+1)=x Γ(x) with Γ(1)=1. Hence Γ(n+1)=n! which is used to generalize the factorial (see Section 11.1.1).
The Gamma command computes the Gamma function.
Gamma(5) |
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Gamma(0.7) |
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Gamma(-0.3) |
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Indeed, Γ(0.7)=−0.3·Γ(−0.3).
Gamma(-1.3) |
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Indeed, Γ(0.7)=−0.3·Γ(−0.3)=−0.3·(−1.3)·Γ(−1.3).