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variants of this functions
Erf






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erf[z] > Integration > Indefinite integration > Involving functions of the direct function and elementary functions > Involving elementary functions of the direct function and elementary functions > Involving products of the direct function and a power function





http://functions.wolfram.com/06.25.21.0126.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) Erf[a z] Erf[b z], z] == (z^\[Alpha] Erf[a z] Erf[b z])/\[Alpha] + (((2 b z^\[Alpha])/(Pi \[Alpha] a)) Sum[(b^(2 k) Gamma[1 + k + \[Alpha]/2, a^2 z^2])/ ((-a^2)^k ((2 k + 1) k!)), {k, 0, Infinity}])/(a^2 z^2)^(\[Alpha]/2) + (((2 a z^\[Alpha])/(Pi \[Alpha] b)) Sum[(a^(2 k) Gamma[1 + k + \[Alpha]/2, b^2 z^2])/ ((-b^2)^k ((2 k + 1) k!)), {k, 0, Infinity}])/(b^2 z^2)^(\[Alpha]/2)










Standard Form





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MathML Form







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</mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> &#945; </mi> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> &#945; </mi> <mn> 2 </mn> </mfrac> </mrow> </msup> <mtext> </mtext> </mrow> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#945; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mfrac> <mrow> <msup> <mi> a </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> k </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> k </mi> <mo> + </mo> <mfrac> <mi> &#945; </mi> <mn> 2 </mn> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> k </mi> <mo> ! 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Rule Form





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





2001-10-29





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