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variants of this functions
InverseErf






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > InverseErf[z] > Series representations > Generalized power series > Expansions at generic point z==z0 > For the function itself





http://functions.wolfram.com/06.29.06.0004.01









  


  










Input Form





InverseErf[z] \[Proportional] InverseErf[Subscript[z, 0]] + (Sqrt[Pi]/2) E^InverseErf[Subscript[z, 0]]^2 (z - Subscript[z, 0]) + (Pi/4) E^(2 InverseErf[Subscript[z, 0]]^2) InverseErf[Subscript[z, 0]] (z - Subscript[z, 0])^2 + (Pi^(3/2)/24) E^(3 InverseErf[Subscript[z, 0]]^2) (1 + 4 InverseErf[Subscript[z, 0]]^2) (z - Subscript[z, 0])^3 + (Pi^2/96) E^(4 InverseErf[Subscript[z, 0]]^2) InverseErf[Subscript[z, 0]] (7 + 12 InverseErf[Subscript[z, 0]]^2) (z - Subscript[z, 0])^4 + (Pi^(5/2)/960) E^(5 InverseErf[Subscript[z, 0]]^2) (7 + 8 InverseErf[Subscript[z, 0]]^2) (1 + 12 InverseErf[Subscript[z, 0]]^2) (z - Subscript[z, 0])^5 + (Pi^3/5760) E^(6 InverseErf[Subscript[z, 0]]^2) InverseErf[Subscript[z, 0]] (127 + 652 InverseErf[Subscript[z, 0]]^2 + 480 InverseErf[Subscript[z, 0]]^4) (z - Subscript[z, 0])^6 + (Pi^(7/2)/80640) E^(7 InverseErf[Subscript[z, 0]]^2) (127 + 3480 InverseErf[Subscript[z, 0]]^2 + 10224 InverseErf[Subscript[z, 0]]^4 + 5760 InverseErf[Subscript[z, 0]]^6) (z - Subscript[z, 0])^7 + (Pi^4/645120) E^(8 InverseErf[Subscript[z, 0]]^2) InverseErf[Subscript[z, 0]] (4369 + 44808 InverseErf[Subscript[z, 0]]^2 + 88848 InverseErf[Subscript[z, 0]]^4 + 40320 InverseErf[Subscript[z, 0]]^6) (z - Subscript[z, 0])^8 + (Pi^(9/2)/11612160) E^(9 InverseErf[Subscript[z, 0]]^2) (4369 + 204328 InverseErf[Subscript[z, 0]]^2 + 1161168 InverseErf[Subscript[z, 0]]^4 + 1703808 InverseErf[Subscript[z, 0]]^6 + 645120 InverseErf[Subscript[z, 0]]^8) (z - Subscript[z, 0])^9 + (Pi^5/116121600) E^(10 InverseErf[Subscript[z, 0]]^2) InverseErf[Subscript[z, 0]] (243649 + 4161288 InverseErf[Subscript[z, 0]]^2 + 15561936 InverseErf[Subscript[z, 0]]^4 + 17914752 InverseErf[Subscript[z, 0]]^6 + 5806080 InverseErf[Subscript[z, 0]]^8) (z - Subscript[z, 0])^10 + \[Ellipsis] /; (z -> Subscript[z, 0])










Standard Form





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MathML Form







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</mrow> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </msup> <mo> &#8290; </mo> <mrow> <msup> <mi> erf </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 40320 </mn> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> erf </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 88848 </mn> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> erf </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 44808 </mn> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> erf </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 4369 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <msup> <mi> &#960; </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mtext> </mtext> </mrow> <mn> 11612160 </mn> </mfrac> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> erf </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 645120 </mn> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> erf </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1703808 </mn> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> erf </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1161168 </mn> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> erf </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 204328 </mn> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> erf </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 4369 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <msup> <mi> &#960; </mi> <mn> 5 </mn> </msup> <mtext> </mtext> </mrow> <mn> 116121600 </mn> </mfrac> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> erf </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </msup> <mo> &#8290; </mo> <mrow> <msup> <mi> erf </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5806080 </mn> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> erf </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 17914752 </mn> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> erf </mi> <mrow> <mo> - 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<power /> <apply> <ci> InverseErf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 17914752 </cn> <apply> <power /> <apply> <ci> InverseErf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 15561936 </cn> <apply> <power /> <apply> <ci> InverseErf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4161288 </cn> <apply> <power /> <apply> <ci> InverseErf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 243649 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <cn type='integer'> 10 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





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