|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/05.05.16.0003.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ChebyshevU[2 n, Sqrt[(1 + z)/2]] == ChebyshevU[n, z] + ChebyshevU[n - 1, z]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["2", "n"]], ",", SqrtBox[FractionBox[RowBox[List["1", "+", "z"]], "2"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["ChebyshevU", "[", RowBox[List["n", ",", "z"]], "]"]], "+", RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", "z"]], "]"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<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> ⁢ </mo> <mi> n </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>  </mo> <mrow> <mrow> <msub> <mi> U </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msub> <mi> U </mi> <mi> n </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> n </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> n </ci> <cn type='integer'> -1 </cn> </apply> <ci> z </ci> </apply> <apply> <ci> ChebyshevU </ci> <ci> n </ci> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["2", " ", "n_"]], ",", SqrtBox[FractionBox[RowBox[List["1", "+", "z_"]], "2"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ChebyshevU", "[", RowBox[List["n", ",", "z"]], "]"]], "+", RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", "z"]], "]"]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
){kind=small}
