1 17 ( ) www The gamma function is defined by (x) 0 ux1e u du (1 141) Using integration by parts, prove the relation (x 1) x(x) Show also that (1) 1 and hence that (x 1) x when x is an integer ...

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1.17 ( ) www The gamma function is defined by (x) 0 ux1e u...

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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.

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