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HypergeometricU






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricU[a,b,z] > Differentiation > Low-order differentiation > With respect to a





http://functions.wolfram.com/07.33.20.0002.01









  


  










Input Form





Derivative[1, 0, 0][HypergeometricU][a, b, z] == (-((z^(1 - b) Gamma[b - 1] PolyGamma[a])/Gamma[a])) Hypergeometric1F1[1 + a - b, 2 - b, z] - ((Gamma[1 - b] PolyGamma[1 + a - b])/Gamma[1 + a - b]) Hypergeometric1F1[a, b, z] - ((z Gamma[-b])/Gamma[1 + a - b]) HypergeometricPFQ[{{1 + a}, {1}, {1, a}}, {{2, 1 + b}, {}, {1 + a}}, z, z] - ((z^(2 - b) Gamma[b - 2])/Gamma[a]) HypergeometricPFQ[ {{2 + a - b}, {1}, {1, 1 + a - b}}, {{2, 3 - b}, {}, {2 + a - b}}, z, z] /; !Element[b, Integers]










Standard Form





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MathML Form







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</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 2 </mn> <mo> , </mo> <mrow> <mrow> <mrow> <mn> 3 </mn> <mo> - </mo> <mi> b </mi> </mrow> <mo> ; </mo> </mrow> <mo> ; </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </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> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





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