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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 cosh





http://functions.wolfram.com/06.25.21.0113.01









  


  










Input Form





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










Standard Form





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MathML Form







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










Rule Form





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





2001-10-29