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Erfi






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erfi[z] > Integration > Indefinite integration > Involving functions of the direct function and elementary functions > Involving elementary functions of the direct function and elementary functions > Involving products of the direct function and a power function





http://functions.wolfram.com/06.28.21.0127.01









  


  










Input Form





Integrate[z^2 Erfi[a z] Erfi[b z], z] == (1/(3 Pi^(3/2))) ((E^((a^2 + b^2) z^2) Sqrt[Pi] z)/(a b) + (Pi z)/(2 a b Sqrt[(-(a^2 + b^2)) z^2]) - (Pi z Erf[Sqrt[(-(a^2 + b^2)) z^2]])/(2 a b Sqrt[(-(a^2 + b^2)) z^2]) + (E^(a^2 z^2) Pi Erfi[b z])/a^3 - (E^(a^2 z^2) Pi z^2 Erfi[b z])/a + (1/b^3) (Pi Erfi[a z] (E^(b^2 z^2) (1 - b^2 z^2) + b^3 Sqrt[Pi] z^3 Erfi[b z])) - (a Pi Erfi[Sqrt[a^2 + b^2] z])/ (b^3 Sqrt[a^2 + b^2]) - (b Pi Erfi[Sqrt[a^2 + b^2] z])/ (a^3 Sqrt[a^2 + b^2]))










Standard Form





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MathML Form







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<ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <pi /> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <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> <pi /> <apply> <ci> Erfi </ci> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> 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<apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





© 1998- Wolfram Research, Inc.