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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 power, exponential and trigonometric functions > Involving power, exp and cos





http://functions.wolfram.com/06.25.21.0066.01









  


  










Input Form





Integrate[z^2 E^(b z) Cos[c z] Erf[a z], z] == ((1/(8 a^4 Sqrt[Pi])) ((1/(b - I c)^3) (2 a (b - I c) E^((b - I c) z) ((b - I c)^2 + 2 a^2 (-2 + b z - I c z)) + 4 a^4 E^(z (b - I c + a^2 z)) Sqrt[Pi] (2 - 2 (b - I c) z + (b - I c)^2 z^2) Erf[a z] + (8 a^4 - 2 a^2 (b - I c)^2 + (b - I c)^4) E^((b - I c)^2/(4 a^2) + a^2 z^2) Sqrt[Pi] Erf[(b - I c)/(2 a) - a z]) + (1/(b + I c)^3) (2 a (b + I c) E^((b + I c) z) ((b + I c)^2 + 2 a^2 (-2 + b z + I c z)) + 4 a^4 E^(z (b + I c + a^2 z)) Sqrt[Pi] (2 - 2 (b + I c) z + (b + I c)^2 z^2) Erf[a z] + (8 a^4 - 2 a^2 (b + I c)^2 + (b + I c)^4) E^((b + I c)^2/(4 a^2) + a^2 z^2) Sqrt[Pi] Erf[(b + I c)/(2 a) - a z])))/E^(a^2 z^2)










Standard Form





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MathML Form







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





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





2001-10-29