sol for exam 2 take home

also know the following 2m 1 2 2m 1 2m where

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Unformatted text preview: ! . Also, know the following: Γ 2m + 1 2 = 2m − 1 ! ! √ π 2m where for m = 0 you should read m : non-negative integer , 2m − 1 !! as 1. 8 (3a) Γ0 = ‘divergent’ Γ , Γ1 = 1 Γ , Γ2 = 1 Γ , Γ3 = 2 Γ , Γ4 = 6 Γ , Γ5 = 24 Γ , 1 2 = 3 2 = 5 2 = 7 2 = 9 2 = 11 2 = √ π , 1√ π 2 , 3√ π 4 , 15 √ π 8 , 105 √ π 16 , 945 √ π 32 . Compare the above with the results of “Extra Credit Homework – VI”. Γ (3b) 3 2 = 1 2 ·Γ 1 2 , Γ2 = 1 · Γ 1), Γ 5 2 = 3 2 ·Γ 3 2 , Γ3 = 2 · Γ 2), Γ 7 2 = 5 2 ·Γ 5 2 , Γ5 = 3 · Γ 3), Γ 9 2 = 7 2 ·Γ 7 2 , Γ5 = 4 · Γ 4), Γ 11 2 = 9 2 ·Γ 9 2 , Γ5 = 5 · Γ 5), Γ 13 2 = 11 2 ·Γ 11 2 9 . (4) (Extra 10pts) Let Γ x be as in (3). Prove that, for an arbitrary real number x with x > 0, the following identity holds: Γ x+1 Proof : = xΓ x. Start with th...
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This note was uploaded on 01/12/2014 for the course MATH 116 taught by Professor Scholle,minho during the Fall '08 term at Kansas.

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