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

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2002-12-18