Integrate[z^3 Sin[b z] Erfc[a z], z] == (1/(16 a^6 b^4 Sqrt[Pi])) (E^(-(b^2/(4 a^2)) - I b z - a^2 z^2) (-48 a^5 b E^(b^2/(4 a^2)) - 4 a^3 b^3 E^(b^2/(4 a^2)) - 2 a b^5 E^(b^2/(4 a^2)) - 48 a^5 b E^((1/4) b (b/a^2 + 8 I z)) - 4 a^3 b^3 E^((1/4) b (b/a^2 + 8 I z)) - 2 a b^5 E^((1/4) b (b/a^2 + 8 I z)) - 24 I a^5 b^2 E^(b^2/(4 a^2)) z - 4 I a^3 b^4 E^(b^2/(4 a^2)) z + 24 I a^5 b^2 E^((1/4) b (b/a^2 + 8 I z)) z + 4 I a^3 b^4 E^((1/4) b (b/a^2 + 8 I z)) z + 8 a^5 b^3 E^(b^2/(4 a^2)) z^2 + 8 a^5 b^3 E^((1/4) b (b/a^2 + 8 I z)) z^2 - I (48 a^6 + 12 a^4 b^2 + b^6) E^(z (I b + a^2 z)) Sqrt[Pi] Erf[(I b + 2 a^2 z)/(2 a)] + 48 a^6 E^(z (I b + a^2 z)) Sqrt[Pi] Erfi[b/(2 a) + I a z] + 12 a^4 b^2 E^(z (I b + a^2 z)) Sqrt[Pi] Erfi[b/(2 a) + I a z] + b^6 E^(z (I b + a^2 z)) Sqrt[Pi] Erfi[b/(2 a) + I a z] - 8 a^6 E^(b^2/(4 a^2) + a^2 z^2) Sqrt[Pi] Erfc[a z] (b z (-6 - 3 I b z + b^2 z^2 + E^(2 I b z) (-6 + 3 I b z + b^2 z^2)) + 12 E^(I b z) Sin[b z])))

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<ci> a </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> </apply> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 48 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erf </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> a </ci> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29