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HypergeometricU






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.33.20.0007.02









  


  










Input Form





Derivative[n, 0, 0][HypergeometricU][a, b, z] == Gamma[1 - b] Sum[D[Pochhammer[a, k]/Gamma[a - b + 1], {a, n}] (z^k/(Pochhammer[b, k] k!)), {k, 0, Infinity}] + Gamma[b - 1] z^(1 - b) Sum[D[Pochhammer[a - b + 1, k]/Gamma[a], {a, n}] (z^k/(Pochhammer[2 - b, k] k!)), {k, 0, Infinity}] /; Element[n, Integers] && n >= 0 && !Element[b, Integers]










Standard Form





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MathML Form







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</mo> </mrow> </mrow> </mfrac> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> &#8712; </mo> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> b </mi> <mo> &#8713; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29