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

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2002-12-18