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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 power, exponential and trigonometric functions > Involving power, exp and sin





http://functions.wolfram.com/06.27.21.0057.01









  


  










Input Form





Integrate[z^2 E^(b z) Sin[c z] Erfc[a z], z] == (1/(b^2 + c^2)^3) (E^(b z) ((-c) (-4 b^3 z - 4 b c^2 z + b^4 z^2 + c^2 (-2 + c^2 z^2) + 2 b^2 (3 + c^2 z^2)) Cos[c z] + (-2 b^4 z + 2 c^4 z + b^5 z^2 + b c^2 (-6 + c^2 z^2) + 2 b^3 (1 + c^2 z^2)) Sin[c z])) - ((I/(8 a^4 Sqrt[Pi])) ((1/(b - I c)^3) (2 a (b - I c) E^((b - I c) z) ((b - I c)^2 + 2 a^2 (-2 + b z - I c z)) + 4 a^4 E^(z (b - I c + a^2 z)) Sqrt[Pi] (2 - 2 (b - I c) z + (b - I c)^2 z^2) Erf[a z] + (8 a^4 - 2 a^2 (b - I c)^2 + (b - I c)^4) E^((b - I c)^2/(4 a^2) + a^2 z^2) Sqrt[Pi] Erf[(b - I c)/(2 a) - a z]) - (1/(b + I c)^3) (2 a (b + I c) E^((b + I c) z) ((b + I c)^2 + 2 a^2 (-2 + b z + I c z)) + 4 a^4 E^(z (b + I c + a^2 z)) Sqrt[Pi] (2 - 2 (b + I c) z + (b + I c)^2 z^2) Erf[a z] + (8 a^4 - 2 a^2 (b + I c)^2 + (b + I c)^4) E^((b + I c)^2/(4 a^2) + a^2 z^2) Sqrt[Pi] Erf[(b + I c)/(2 a) - a z])))/E^(a^2 z^2)










Standard Form





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MathML Form







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</mn> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> erf </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </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> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> 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<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> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erf </ci> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> c </ci> <imaginaryi /> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </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





© 1998-2014 Wolfram Research, Inc.