Integrate[E^(d z + e) Cos[c Sqrt[z] + f z + g]^v, z] == (E^(e + d z) Binomial[v, v/2] (1 - Mod[v, 2]))/(2^v d) + Sum[Binomial[v, k] (E^((1/2) (2 e + 4 I g k - 2 I g v) + (2 I c k - I c v) Sqrt[z] + (d + 2 I f k - I f v) z)/ (d + 2 I f k - I f v) + E^((1/2) (2 e - 4 I g k + 2 I g v) + (-2 I c k + I c v) Sqrt[z] + (d - 2 I f k + I f v) z)/ (d - 2 I f k + I f v) - (E^(e + 2 I g k + (c^2 (2 k - v)^2)/(4 (d + I f (2 k - v))) - I g v) Sqrt[Pi] (2 I c k - I c v) Erfi[(I c (2 k - v) + 2 (d + 2 I f k - I f v) Sqrt[z])/(2 Sqrt[d + 2 I f k - I f v])])/ (2 (d + 2 I f k - I f v)^(3/2)) - (I c E^(e - 2 I g k + I g v + (c^2 (-2 k + v)^2)/ (4 (d + I f (-2 k + v)))) Sqrt[Pi] (-2 k + v) Erfi[(I c (-2 k + v) + 2 (d - 2 I f k + I f v) Sqrt[z])/ (2 Sqrt[d + I f (-2 k + v)])])/(2 (d - 2 I f k + I f v)^(3/2))), {k, 0, Floor[(1/2) (-1 + v)]}]/2^v /; Element[v, Integers] && v > 0

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2002-12-18