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variants of this functions
Hypergeometric2F1Regularized






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Differentiation > Symbolic differentiation > With respect to z





http://functions.wolfram.com/07.24.20.0043.02









  


  










Input Form





D[z^\[Alpha] Hypergeometric2F1Regularized[-(n/2), (-n + 1)/2, c, z^m], {z, n}] == m^(n - 1/2 - \[Alpha]) Gamma[\[Alpha] + 1] (2 Pi)^((m - 1)/2) z^(\[Alpha] - n) HypergeometricPFQRegularized[{-(n/2), (-n + 1)/2, (\[Alpha] + 1)/m, (\[Alpha] + 2)/m, \[Ellipsis], (\[Alpha] + m)/m}, {(\[Alpha] - n + 1)/m, (\[Alpha] - n + 2)/m, \[Ellipsis], (\[Alpha] - n + m)/m, c}, z^m] /; Element[m, Integers] && m > 0 && Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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</ms> <ms> - </ms> <ms> n </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> <ms> m </ms> </apply> </list> </apply> <ms> , </ms> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> &#945; </ms> <ms> - </ms> <ms> n </ms> <ms> + </ms> <ms> 2 </ms> </list> </apply> <ms> m </ms> </apply> <ms> , </ms> <ms> &#8230; </ms> <ms> , </ms> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> &#945; </ms> <ms> - </ms> <ms> n </ms> <ms> + </ms> <ms> m </ms> </list> </apply> <ms> m </ms> </apply> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <ms> c </ms> <ms> ; </ms> <apply> <ci> TagBox </ci> <apply> <ci> SuperscriptBox </ci> <ms> z </ms> <ms> m </ms> </apply> <ci> HypergeometricPFQ </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> </list> </apply> <ms> /; </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> m </ms> <ms> &#8712; 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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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