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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Differentiation > Low-order differentiation > With respect to b





http://functions.wolfram.com/07.23.20.0051.01









  


  








Input Form





Derivative[0, 1, 0, 0][Hypergeometric2F1][1, c, c, z] == (z/(1 - z)) LerchPhiClassical[z, 1, c]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["Derivative", "[", RowBox[List["0", ",", "1", ",", "0", ",", "0"]], "]"]], "[", "Hypergeometric2F1", "]"]], "[", RowBox[List["1", ",", "c", ",", "c", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["z", " "]], RowBox[List["1", "-", "z"]]], RowBox[List["LerchPhiClassical", "[", RowBox[List["z", ",", "1", ",", "c"]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> Hypergeometric2F1 </mi> <semantics> <mrow> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;0&quot;, &quot;,&quot;, &quot;1&quot;, &quot;,&quot;, &quot;0&quot;, &quot;,&quot;, &quot;0&quot;]], &quot;)&quot;]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> c </mi> <mo> , </mo> <mi> c </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mrow> <mi> z </mi> <mtext> </mtext> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mover> <mi> &#934; </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 1 </cn> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> </list> <ci> Hypergeometric2F1 </ci> </apply> <cn type='integer'> 1 </cn> <ci> c </ci> <ci> c </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <apply> <ci> OverHat </ci> <ci> &#934; </ci> </apply> <ci> z </ci> <cn type='integer'> 1 </cn> <ci> c </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox["Hypergeometric2F1", TagBox[RowBox[List["(", RowBox[List["0", ",", "1", ",", "0", ",", "0"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["1", ",", "c_", ",", "c_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["z", " ", RowBox[List["LerchPhiClassical", "[", RowBox[List["z", ",", "1", ",", "c"]], "]"]]]], RowBox[List["1", "-", "z"]]]]]]]










Contributed by





Brychkov Yu.A. (2006)


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





2007-05-02