Page 178 - Essentials of applied mathematics for scientists and engineers

book Mobk070 March 22, 2007 11:7

168 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS

1 2
49 K 0 (qx) e −x /4α t
2t
1 1 −x 8α t x 2
2
50 K 2v (qx) e K v
p 1/2 2(πt) 1/2 8αt
2
α
51 p v/2−1 K v (qx) x −v v/2 v−1 ∞ e −u v−1 du
u
x 2 /4α t
x v −x /4α t
2
v/2
52 p K v (qx) e
α v/2 (2t) v+1
x v
2 2 1/2
v
53 p − (p − x ) v I v (xt)
t
1/2 z
54 e x[(p+α) 1/2 −(p+β) ] − 1 x(α − β)e −(α+β)t/2 I 1 1 2 (α − β)t 1/2 (t + 4x) 1/2
t 1/2 (t + 4x) 1/2
1/2
e x[ p−(p+α) 1/2 (p+β) ]
55 e −(α+β)(t+x)/2 I 0 1 (α − β)t 1/2 (t + 2x) 1/2
(p + α) 1/2 (p + β) 1/2 2
1/2 2
e
e x[(p+α) 1/2 −(p+β) ] t v/2 −(α+β)t/2 I v 1 (α − β)t 1/2 (t + 4x) 1/2
56
2v 2 v v/2
(p + α) 1/2 (p + β) 1/2 (p + α) 1/2 + (p + β) 1/2 (α − β) (t + 4x)