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Coth




Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Transformations > Multiple arguments > Argument involving symbolic multiples of variable





http://functions.wolfram.com/01.22.16.0043.01









  


  








Input Form





Coth[n z] == ChebyshevT[n, Cosh[z]]/(Sinh[z] ChebyshevU[n - 1, Cosh[z]])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Coth", "[", RowBox[List["n", " ", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List["ChebyshevT", "[", RowBox[List["n", ",", RowBox[List["Cosh", "[", "z", "]"]]]], "]"]], RowBox[List[RowBox[List["Sinh", "[", "z", "]"]], " ", RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", RowBox[List["Cosh", "[", "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> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <msub> <mi> T </mi> <mi> n </mi> </msub> <mo> ( </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> U </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <coth /> <apply> <times /> <ci> n </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <ci> ChebyshevT </ci> <ci> n </ci> <apply> <cosh /> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <sinh /> <ci> z </ci> </apply> <apply> <ci> ChebyshevU </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <apply> <cosh /> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Coth", "[", RowBox[List["n_", " ", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["ChebyshevT", "[", RowBox[List["n", ",", RowBox[List["Cosh", "[", "z", "]"]]]], "]"]], RowBox[List[RowBox[List["Sinh", "[", "z", "]"]], " ", RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", RowBox[List["Cosh", "[", "z", "]"]]]], "]"]]]]]]]]]


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





2001-10-29