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variants of this functions
InverseErf




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > InverseErf[z1,z2] > Differentiation > Symbolic differentiation > With respect to z2





http://functions.wolfram.com/06.30.20.0005.01









  


  








Input Form





D[InverseErf[Subscript[z, 1], Subscript[z, 2]], {Subscript[z, 2], n}] == KroneckerDelta[n] InverseErf[Subscript[z, 1], Subscript[z, 2]] + (Pi^(n/2)/2^n) E^(n InverseErf[Subscript[z, 1], Subscript[z, 2]]^2) Sum[\[Ellipsis] Sum[KroneckerDelta[Sum[(i - 1) Subscript[j, i], {i, 2, n}], n - 1] (-1)^Sum[Subscript[j, i], {i, 2, n}] (n - 1 + Sum[Subscript[j, i], {i, 2, n}])! Product[(1/Subscript[j, i]!) ((2^(-1 + i) E^InverseErf[Subscript[z, 1], Subscript[z, 2]]^2 Sqrt[Pi] InverseErf[Subscript[z, 1], Subscript[z, 2]]^(1 - i))/ i!)^Subscript[j, i] HypergeometricPFQRegularized[{1/2, 1}, {1 - i/2, (3 - i)/2}, -InverseErf[Subscript[z, 1], Subscript[z, 2]]^2]^Subscript[j, i], {i, 2, n}], {Subscript[j, n], 0, n}], {Subscript[j, 2], 0, n}] /; Element[n, Integers] && n >= 0








Standard Form





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MathML Form







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</ci> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <ci> j </ci> <ci> n </ci> </apply> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <ci> KroneckerDelta </ci> <apply> <sum /> <bvar> <ci> i </ci> </bvar> <lowlimit> <cn type='integer'> 2 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <plus /> <ci> i </ci> <cn type='integer'> -1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <ci> i </ci> </apply> </apply> </apply> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <sum /> <bvar> <ci> i </ci> </bvar> <lowlimit> <cn type='integer'> 2 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <ci> Subscript </ci> <ci> j </ci> <ci> i </ci> </apply> </apply> </apply> <apply> <factorial /> <apply> <plus /> <ci> n </ci> <apply> <sum /> <bvar> <ci> i </ci> </bvar> <lowlimit> <cn type='integer'> 2 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <ci> Subscript </ci> <ci> j </ci> <ci> i </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <product /> <bvar> <ci> i </ci> </bvar> <lowlimit> <cn type='integer'> 2 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <factorial /> <apply> <ci> Subscript </ci> <ci> j </ci> <ci> i </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> i </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <power /> <apply> <ci> InverseErf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> InverseErf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> i </ci> </apply> </apply> </apply> <apply> <power /> <apply> <factorial /> <ci> i </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <ci> i </ci> </apply> </apply> <apply> <power /> <apply> <ci> HypergeometricPFQRegularized </ci> <list> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='integer'> 1 </cn> </list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> i </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> i </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <ci> InverseErf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <ci> i </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02