Integrate[Sinh[b z^2]^m Cosh[c z^2 + f z], z] == -((1/c) ((I^m 2^(-2 - m) Sqrt[Pi] Binomial[m, m/2] (Sqrt[-c] E^(f^2/(2 c)) Erfi[(Sqrt[-c] (f + 2 c z))/(2 c)] - Sqrt[c] Erfi[(f + 2 c z)/(2 Sqrt[c])]) (1 - Mod[m, 2]))/ E^(f^2/(4 c)))) + 2^(-2 - m) Sqrt[Pi] Sum[(-1)^k Binomial[m, k] (-(((-1)^m Sqrt[-c + 2 b k - b m] Erfi[(-f - 2 c z + 4 b k z - 2 b m z)/ (2 Sqrt[-c + 2 b k - b m])])/E^(f^2/(-4 c + 8 b k - 4 b m))/ (c + b (-2 k + m))) + (1/(-c - 2 b k + b m)) (((-(-1)^m) Sqrt[c + 2 b k - b m] Erfi[(f + 2 c z + 4 b k z - 2 b m z)/(2 Sqrt[c + 2 b k - b m])] + E^(f^2/(2 c + 4 b k - 2 b m)) Sqrt[-c - 2 b k + b m] Erfi[(-f - 2 c z - 4 b k z + 2 b m z)/(2 Sqrt[-c - 2 b k + b m])])/ E^(f^2/(4 c + 8 b k - 4 b m))) + (E^(f^2/(-4 c + 8 b k - 4 b m)) Erfi[(f + 2 c z - 4 b k z + 2 b m z)/(2 Sqrt[c + b (-2 k + m)])])/ Sqrt[c + b (-2 k + m)]), {k, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0

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2002-12-18