D[JacobiP[\[Nu], a, b, z], {z, m}] == (Pochhammer[a + b + \[Nu] + 1, m] JacobiP[\[Nu] - m, a + m, b + m, z])/ 2^m /; Element[m, Integers] && m > 0

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mi> m </mi> </msup> <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> <msup> <mi> z </mi> <mi> m </mi> </msup> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <msup> <mn> 2 </mn> <mrow> <mo> - </mo> <mi> m </mi> </mrow> </msup> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> m </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;a&quot;, &quot;+&quot;, &quot;b&quot;, &quot;+&quot;, &quot;\[Nu]&quot;, &quot;+&quot;, &quot;1&quot;]], &quot;)&quot;]], &quot;m&quot;], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <msubsup> <mi> P </mi> <mrow> <mi> &#957; </mi> <mo> - </mo> <mi> m </mi> </mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mi> m </mi> </mrow> <mo> , </mo> <mrow> <mi> b </mi> <mo> + </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> m </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <ci> m </ci> </degree> </bvar> <apply> <ci> JacobiP </ci> <ci> &#957; </ci> <ci> a </ci> <ci> b </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <ci> a </ci> <ci> b </ci> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <ci> m </ci> </apply> <apply> <ci> JacobiP </ci> <apply> <plus /> <ci> &#957; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <apply> <plus /> <ci> a </ci> <ci> m </ci> </apply> <apply> <plus /> <ci> b </ci> <ci> m </ci> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <in /> <ci> m </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29