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variants of this functions
ChebyshevT




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ChebyshevT[nu,z] > Integration > Indefinite integration > Involving only one direct function with respect to nu





http://functions.wolfram.com/07.04.21.0006.01









  


  








Input Form





Integrate[ChebyshevT[\[Nu], z], \[Nu]] == (Sqrt[1 - z^2] ChebyshevU[\[Nu] - 1, z])/ArcCos[z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["ChebyshevT", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], RowBox[List["\[DifferentialD]", "\[Nu]"]]]]]], "\[Equal]", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", " ", "-", " ", SuperscriptBox["z", RowBox[List[" ", "2"]]]]]], RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["\[Nu]", "-", "1"]], ",", "z"]], "]"]]]], RowBox[List["ArcCos", "[", "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> <mo> &#8747; </mo> <mrow> <mrow> <msub> <mi> T </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> &#957; </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mrow> <msup> <mi> cos </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <msub> <mi> U </mi> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> &#957; </ci> </bvar> <apply> <ci> ChebyshevT </ci> <ci> &#957; </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <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> <apply> <power /> <apply> <arccos /> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> ChebyshevU </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["ChebyshevT", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], RowBox[List["\[DifferentialD]", "\[Nu]_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], " ", RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["\[Nu]", "-", "1"]], ",", "z"]], "]"]]]], RowBox[List["ArcCos", "[", "z", "]"]]]]]]]


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





2001-10-29