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variants of this functions
GegenbauerC




Mathematica Notation

Traditional Notation









Hypergeometric Functions > GegenbauerC[nu,z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself > With respect to z





http://functions.wolfram.com/07.13.13.0020.01









  


  








Input Form





Wronskian[h[z] GegenbauerC[\[Nu], g[z]], h[z] Sqrt[1 - g[z]^2] ChebyshevU[\[Nu] - 1, g[z]], z] == -((2 h[z]^2 Derivative[1][g][z])/Sqrt[1 - g[z]^2])








Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> W </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> h </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msubsup> <mi> C </mi> <mi> &#957; </mi> <mrow> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mrow> <mi> g </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mrow> <mi> h </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mrow> <mi> g </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <msub> <mi> U </mi> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <mi> g </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mrow> <mi> h </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <msup> <mi> g </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mrow> <mi> g </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </msqrt> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <ci> h </ci> <ci> z </ci> </apply> <apply> <ci> GegenbauerC </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <ci> h </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <ci> g </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> ChebyshevU </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <ci> h </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <ci> g </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02