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

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2002-12-18