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Erfc






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erfc[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions and a power function > Involving cos and power





http://functions.wolfram.com/06.27.21.0046.01









  


  










Input Form





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










Standard Form





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MathML Form







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</apply> </apply> </apply> <apply> <ci> Erfc </ci> <apply> <plus /> <ci> c </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <ci> b </ci> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='complex-cartesian'> 1 <sep /> -1 </cn> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <exp /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <ci> b </ci> 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type='complex-cartesian'> 2 <sep /> 2 </cn> <apply> <ci> Erfc </ci> <apply> <plus /> <ci> c </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </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





© 1998- Wolfram Research, Inc.