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http://functions.wolfram.com/07.04.06.0001.02
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ChebyshevT[\[Nu], z] \[Proportional] 1 - (ArcCos[z]^2/2) \[Nu]^2 +
(ArcCos[z]^4/24) \[Nu]^4 - \[Ellipsis] /; (\[Nu] -> 0)
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ChebyshevT", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List["1", "-", RowBox[List[FractionBox[RowBox[List[" ", SuperscriptBox[RowBox[List["ArcCos", "[", "z", "]"]], "2"]]], "2"], " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["ArcCos", "[", "z", "]"]], "4"], "24"], " ", SuperscriptBox["\[Nu]", "4"]]], "-", "\[Ellipsis]"]]]], "/;", RowBox[List["(", RowBox[List["\[Nu]", "\[Rule]", "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> <mrow> <msub> <mi> T </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mfrac> <mrow> <mtext> </mtext> <mrow> <msup> <mi> cos </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mrow> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> ν </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <msup> <mrow> <msup> <mi> cos </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mn> 24 </mn> </mfrac> <mo> ⁢ </mo> <mtext> </mtext> <msup> <mi> ν </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mo> … </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> ChebyshevT </ci> <ci> ν </ci> <ci> z </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <ci> cos </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> ν </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <apply> <arccos /> <ci> z </ci> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <cn type='integer'> 24 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> ν </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> … </ci> </apply> </apply> </apply> <apply> <ci> Rule </ci> <ci> ν </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ChebyshevT", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["1", "-", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["ArcCos", "[", "z", "]"]], "2"], " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List[FractionBox["1", "24"], " ", SuperscriptBox[RowBox[List["ArcCos", "[", "z", "]"]], "4"], " ", SuperscriptBox["\[Nu]", "4"]]], "-", "\[Ellipsis]"]], "/;", RowBox[List["(", RowBox[List["\[Nu]", "\[Rule]", "0"]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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