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

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2002-12-18