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Coth




Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Transformations > Products, sums, and powers of the direct function > Sums of the direct function





http://functions.wolfram.com/01.22.16.0047.01









  


  








Input Form





Coth[a] - Coth[b] == (-Csch[a]) Csch[b] Sinh[a - b]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Coth", "[", "a", "]"]], "-", RowBox[List["Coth", "[", "b", "]"]]]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List["Csch", "[", "a", "]"]]]], " ", RowBox[List["Csch", "[", "b", "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["a", "-", "b"]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mrow> <mi> csch </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mi> csch </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <coth /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <coth /> <ci> b </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <csch /> <ci> a </ci> </apply> </apply> <apply> <csch /> <ci> b </ci> </apply> <apply> <sinh /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Coth", "[", "a_", "]"]], "-", RowBox[List["Coth", "[", "b_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", RowBox[List["Csch", "[", "a", "]"]]]], " ", RowBox[List["Csch", "[", "b", "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["a", "-", "b"]], "]"]]]]]]]]


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





2001-10-29