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

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<plus /> <ci> b </ci> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> p </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> p </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> 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2002-12-18