Mathematic Methods HW Solutions 53

Mathematic Methods HW Solutions 53 - Chapter 11 3.2 3.5 3.8...

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Unformatted text preview: Chapter 11 3.2 3.5 3.8 3.11 3.14 3/2 32/35 Γ(5/3) 1 −Γ(4/3) 3.3 3.6 3.9 3.12 3.15 9/10 72 Γ(5/4) Γ(2/3)/3 Γ(2/3)/4 1 7.1 2 B (5/2, 1/2) = 3π/16 1 7.3 3 B (1/3, 1/2) 7.5 B (3, 3) = 1/30 1 7.7 2 B (1/4, 1/2) 7.10 4 B (1/3, 4/3) 3 √ 7.12 (8π/3)B (5/3, 1/3) = 32π 2 3/27 7.13 Iy /M = 8B (4/3, 4/3)/B (5/3, 1/3) 8.1 25/14 8 Γ(3/5) 3−4 Γ(4) = 2/27 Γ(p) √ 1 7.2 2 B (5/4, 3/4) = π 2/8 1 7.4 2 B (3/2, 5/2) = π/32 √ 1 7.6 B 3√ (2/3, 4/3) = 2π √3/27 7.8 4 2B (3, 1/2) = 64 2/15 7.11 2B (2/3, 4/3)/B (1/3, 4/3) B (1/2, 1/4) 2l/g = 7.4163 l/g 8.2 8.3 3.4 3.7 3.10 3.13 3.17 1 4 Compare 2π l/g . 35/11 B (1/2, 1/4) = 2.34 sec t = π a/g 10.2 Γ(p, x) ∼ xp−1 e−x [1 +√p − 1)x−1 + (p − 1)(p − 2)x−2 + · · · ] ( 10.3 erfc (x) = Γ 1/2, x2 / π 10.5 (a) E1 (x) = Γ(0, x) (b) Γ(0, x) ∼ x−1 e−x [1 − x−1 + 2x−2 − 3! x−3 + · · · ] 10.6 (a) Ei(ln x) (b) Ei(x) (c) − Ei(ln x) √ 11.4 1/ π 11.5 1 11.10 e−1 12.1 K = F (π/2, k ) = (π/2) 1 + E = E (π/2, k ) = (π/2) 1 − 122 2k 122 2k + − 1·3 2 4 2·4 k 12 2·4 + ··· · 3k 4 − 1·3 2 2·4·6 · 5k 6 · · · Caution : For the following answers, see the text warning about elliptic integral notation just after equations (12.3) and in Example 1. 12.4 K (1/2) ∼ 1.686 12.5 E (1/3) ∼ 1.526 = = 1 π π1∼ 12.6 3 F 3 , 3 = 0.355 12.7 5E 54 , 1 ∼ 19.46 = √5 12.9 F π , 3 ∼ 0.542 12.8 7E π , 2 ∼ 7.242 = = 3 12.10 1 2F 12.12 10E 7 π1∼ 4 , 2 = 0.402 π1∼ 6 , 10 = 5.234 6 12.11 F 12.13 3E 53 2 3π √3 8 , 10 π2 6, 3 + ∼ 4.097 = 32∼ 3E arc sin 4 , 3 = 3.96 +K √3 10 ...
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