1.17 ( ) www The gamma function is defined by (x) 0 ux1e u du. (1.141) Using integration by parts, prove the

1.17 (

) www The gamma function is defined by

Γ(x) ≡

 ∞

0 ux−1e

−u du. (1.141)

Using integration by parts, prove the relation Γ(x + 1) = xΓ(x). Show also that

Γ(1) = 1 and hence that Γ(x + 1) = x! when x is an integer.