Integrate[E^(p z) Cos[b Sqrt[z]]^m Sinh[c z], z] == 2^(-1 - m) (E^((-c + p) z)/(c - p) + E^((c + p) z)/(c + p)) Binomial[m, m/2] (1 - Mod[m, 2]) + 2^(-1 - m) Sum[Binomial[m, j] ((4 E^(p z) Cos[b (2 j - m) Sqrt[z]] ((-c) Cosh[c z] + p Sinh[c z]))/(-c^2 + p^2) + (1/(2 (-c + p)^(3/2))) (I E^((b^2 (-2 j + m)^2)/(4 (-c + p))) (2 b j - b m) Sqrt[Pi] Erfi[(2 I b j - I b m - 2 c Sqrt[z] + 2 p Sqrt[z])/(2 Sqrt[-c + p])]) - (1/(2 (-c + p)^(3/2))) (I E^((b^2 (-2 j + m)^2)/(4 (-c + p))) (2 b j - b m) Sqrt[Pi] Erfi[(-2 I b j + I b m - 2 c Sqrt[z] + 2 p Sqrt[z])/ (2 Sqrt[-c + p])]) - (I b E^((b^2 (-2 j + m)^2)/(4 (c + p))) (2 j - m) Sqrt[Pi] Erfi[(2 I b j - I b m + 2 c Sqrt[z] + 2 p Sqrt[z])/(2 Sqrt[c + p])])/(2 (c + p)^(3/2)) + (1/(2 (c + p)^(3/2))) (I E^((b^2 (-2 j + m)^2)/(4 (c + p))) (2 b j - b m) Sqrt[Pi] Erfi[(-2 I b j + I b m + 2 c Sqrt[z] + 2 p Sqrt[z])/(2 Sqrt[c + p])])), {j, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0

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2002-12-18