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

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2002-12-18