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variants of this functions
Erf






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erf[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions and a power function > Involving cos and power





http://functions.wolfram.com/06.25.21.0045.01









  


  










Input Form





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










Standard Form





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MathML Form







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</cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <ci> b </ci> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <power /> <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> z </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <power /> <ci> b </ci> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <ci> b </ci> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <power /> <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> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <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> 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29





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