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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 hyperbolic functions > Involving power, exp and sinh





http://functions.wolfram.com/06.25.21.0101.01









  


  










Input Form





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










Standard Form





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MathML Form







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<mi> b </mi> <mo> - </mo> <mi> c </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> </mfrac> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <ci> z </ci> <apply> <power /> <exponentiale /> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> <apply> <sinh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <ci> Erf </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> 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</apply> </apply> </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





© 1998-2014 Wolfram Research, Inc.