AEM_3e_Appendix2

AEM_3e_Appendix2 - ¯ ¯ ∞ − Z ∞ xt x − 1 − e −...

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Appendices Appendix II Gamma Function 3. If t = x 3 , then dt =3 x 2 dx and x 4 dx = 1 3 t 2 / 3 dt .Now Z 0 x 4 e x 3 dx = Z 0 1 3 t 2 / 3 e t dt = 1 3 Z 0 t 2 / 3 e t dt = 1 3 Γ µ 5 3 = 1 3 (0 . 89) 0 . 297 . 6. For x> 0 Γ( x +1)= Z 0 t x e t dt u = t x ,du = xt x 1 dt ; dv = e t dt, v = e t = t x e t ¯ ¯
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Unformatted text preview: ¯ ¯ ∞ − Z ∞ xt x − 1 ( − e − t ) dt = x Z ∞ t x − 1 e − t dt = x Γ( x ) . 310...
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This note was uploaded on 01/03/2011 for the course BIS 511 taught by Professor Theodoreholford during the Fall '10 term at Yale.

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