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variants of this functions
ChebyshevU




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ChebyshevU[nu,z] > Transformations > Multiple arguments





http://functions.wolfram.com/07.05.16.0003.01









  


  








Input Form





ChebyshevU[2 \[Nu], Sqrt[(1 + z)/2]] == ChebyshevU[\[Nu], z] + ChebyshevU[\[Nu] - 1, z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["2", "\[Nu]"]], ",", SqrtBox[FractionBox[RowBox[List["1", "+", "z"]], "2"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["ChebyshevU", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "+", RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["\[Nu]", "-", "1"]], ",", "z"]], "]"]]]]]]]]








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> U </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </msub> <mo> ( </mo> <msqrt> <mfrac> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> </msqrt> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mrow> <msub> <mi> U </mi> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msub> <mi> U </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> ChebyshevU </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <plus /> <apply> <ci> ChebyshevU </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> <ci> z </ci> </apply> <apply> <ci> ChebyshevU </ci> <ci> &#957; </ci> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["2", " ", "\[Nu]_"]], ",", SqrtBox[FractionBox[RowBox[List["1", "+", "z_"]], "2"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ChebyshevU", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "+", RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["\[Nu]", "-", "1"]], ",", "z"]], "]"]]]]]]]]


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





2007-05-02