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

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type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <ci> k </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> 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2001-10-29