Integrate[E^(p z^2) Cos[b z^2]^m Sinh[c z], z] == (((2^(-2 - m) Sqrt[Pi])/Sqrt[p]) Binomial[m, m/2] (Erfi[(c - 2 p z)/(2 Sqrt[p])] + Erfi[(c + 2 p z)/(2 Sqrt[p])]) (1 - Mod[m, 2]))/E^(c^2/(4 p)) + 2^(-2 - m) (-1)^(1/4) Sqrt[Pi] Sum[Binomial[m, j] E^((I c^2)/(-8 b j + 4 b m - 4 I p)) ((Sqrt[2 b j - b m - I p] Erfi[((-1)^(1/4) (c + 2 I (2 b j - b m + I p) z))/(2 Sqrt[2 b j - b m + I p])] - I E^((I b c^2 (2 j - m))/(2 (b^2 (-2 j + m)^2 + p^2))) Sqrt[2 b j - b m + I p] Erfi[((-1)^(1/4) ((-I) c + 4 b j z - 2 b m z - 2 I p z))/(2 Sqrt[2 b j - b m - I p])] + I E^((I b c^2 (2 j - m))/(2 (b^2 (-2 j + m)^2 + p^2))) Sqrt[2 b j - b m + I p] Erfi[((-1)^(1/4) (I c + 4 b j z - 2 b m z - 2 I p z))/(2 Sqrt[2 b j - b m - I p])] - Sqrt[2 b j - b m - I p] Erfi[((-1)^(3/4) (I c + 4 b j z - 2 b m z + 2 I p z))/ (2 Sqrt[2 b j - b m + I p])])/(Sqrt[2 b j - b m - I p] Sqrt[2 b j - b m + I p])), {j, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0

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2002-12-18