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Erfi






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erfi[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving power, exponential and hyperbolic functions > Involving power, exp and cosh





http://functions.wolfram.com/06.28.21.0109.01









  


  










Input Form





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










Standard Form





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MathML Form







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<ci> b </ci> <ci> c </ci> </apply> <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> <ci> z </ci> </apply> </apply> </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





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