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variants of this functions
ChebyshevT




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.04.13.0011.01









  


  








Input Form





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








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[RowBox[List["h", "[", "\[Nu]", "]"]], RowBox[List["ChebyshevT", "[", RowBox[List[RowBox[List["g", "[", "\[Nu]", "]"]], ",", "z"]], "]"]]]], ",", " ", RowBox[List[RowBox[List["h", "[", "\[Nu]", "]"]], RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["g", "[", "\[Nu]", "]"]], ",", "z"]], "]"]]]], ",", "\[Nu]"]], "]"]], "\[Equal]", FractionBox[RowBox[List["z", " ", RowBox[List["ArcCos", "[", "z", "]"]], " ", SuperscriptBox[RowBox[List["h", "[", "\[Nu]", "]"]], "2"], " ", RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "\[Nu]", "]"]]]], SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]]]]]








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> &#957; </mi> </msub> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> h </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#957; </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> T </mi> <mrow> <mi> g </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#957; </mi> <mo> ) </mo> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mrow> <mi> h </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#957; </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> U </mi> <mrow> <mi> g </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#957; </mi> <mo> ) </mo> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> cos </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mi> h </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#957; </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <msup> <mi> g </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> &#957; </mi> <mo> ) </mo> </mrow> </mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <ci> &#957; </ci> </apply> <apply> <times /> <apply> <ci> h </ci> <ci> &#957; </ci> </apply> <apply> <ci> ChebyshevT </ci> <apply> <ci> g </ci> <ci> &#957; </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <ci> h </ci> <ci> &#957; </ci> </apply> <apply> <ci> ChebyshevU </ci> <apply> <ci> g </ci> <ci> &#957; </ci> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <ci> z </ci> <apply> <arccos /> <ci> z </ci> </apply> <apply> <power /> <apply> <ci> h </ci> <ci> &#957; </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <partialdiff /> <bvar> <ci> &#957; </ci> </bvar> <apply> <ci> g </ci> <ci> &#957; </ci> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[RowBox[List["h", "[", "\[Nu]_", "]"]], " ", RowBox[List["ChebyshevT", "[", RowBox[List[RowBox[List["g", "[", "\[Nu]_", "]"]], ",", "z_"]], "]"]]]], ",", RowBox[List[RowBox[List["h", "[", "\[Nu]_", "]"]], " ", RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["g", "[", "\[Nu]_", "]"]], ",", "z_"]], "]"]]]], ",", "\[Nu]_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["z", " ", RowBox[List["ArcCos", "[", "z", "]"]], " ", SuperscriptBox[RowBox[List["h", "[", "\[Nu]", "]"]], "2"], " ", RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "\[Nu]", "]"]]]], SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]]]]]


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





2007-05-02