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variants of this functions
Hypergeometric1F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric1F1[a,b,z] > Differentiation > Symbolic differentiation > With respect to z





http://functions.wolfram.com/07.20.20.0014.02









  


  








Input Form





D[z^\[Alpha] Hypergeometric1F1[a, b, z], {z, n}] == (-1)^n Pochhammer[-\[Alpha], n] z^(\[Alpha] - n) HypergeometricPFQ[{\[Alpha] + 1, a}, {\[Alpha] - n + 1, b}, z] /; Element[n, Integers] && n >= 0








Standard Form





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MathML Form







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</mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <ci> n </ci> </degree> </bvar> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> &#945; </ci> </apply> <apply> <ci> Hypergeometric1F1 </ci> <ci> a </ci> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; </ci> </apply> <ci> n </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> &#945; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <plus /> <ci> &#945; </ci> <cn type='integer'> 1 </cn> </apply> <ci> a </ci> </list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <ci> &#945; 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Rule Form





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





2001-10-29