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variants of this functions
JacobiP




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.15.20.0004.01









  


  








Input Form





D[JacobiP[\[Nu], a, b, z], z] == ((1 + a + b + \[Nu])/2) JacobiP[\[Nu] - 1, 1 + a, 1 + b, z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["JacobiP", "[", RowBox[List["\[Nu]", ",", "a", ",", "b", ",", "z"]], "]"]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["1", "+", "a", "+", "b", "+", "\[Nu]"]], "2"], RowBox[List["JacobiP", "[", RowBox[List[RowBox[List["\[Nu]", "-", "1"]], ",", RowBox[List["1", "+", "a"]], ",", RowBox[List["1", "+", "b"]], ",", "z"]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <msubsup> <mi> P </mi> <mi> &#957; </mi> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <mfrac> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <msubsup> <mi> P </mi> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mi> b </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> JacobiP </ci> <ci> &#957; </ci> <ci> a </ci> <ci> b </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> JacobiP </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["JacobiP", "[", RowBox[List["\[Nu]_", ",", "a_", ",", "b_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "a", "+", "b", "+", "\[Nu]"]], ")"]], " ", RowBox[List["JacobiP", "[", RowBox[List[RowBox[List["\[Nu]", "-", "1"]], ",", RowBox[List["1", "+", "a"]], ",", RowBox[List["1", "+", "b"]], ",", "z"]], "]"]]]]]]]]


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





2001-10-29