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Tanh




Mathematica Notation

Traditional Notation









Elementary Functions > Tanh[z] > Transformations > Addition formulas





http://functions.wolfram.com/01.21.16.0031.01









  


  








Input Form





Tanh[a - b] == (Tanh[a] - Tanh[b])/(1 - Tanh[a] Tanh[b])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Tanh", "[", RowBox[List["a", "-", "b"]], "]"]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["Tanh", "[", "a", "]"]], "-", RowBox[List["Tanh", "[", "b", "]"]]]], RowBox[List["1", "-", RowBox[List[RowBox[List["Tanh", "[", "a", "]"]], " ", RowBox[List["Tanh", "[", "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> <mi> tanh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mrow> <mi> tanh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> tanh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mrow> <mi> tanh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> tanh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <tanh /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <tanh /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <tanh /> <ci> b </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <tanh /> <ci> a </ci> </apply> <apply> <tanh /> <ci> b </ci> </apply> </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["Tanh", "[", RowBox[List["a_", "-", "b_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["Tanh", "[", "a", "]"]], "-", RowBox[List["Tanh", "[", "b", "]"]]]], RowBox[List["1", "-", RowBox[List[RowBox[List["Tanh", "[", "a", "]"]], " ", RowBox[List["Tanh", "[", "b", "]"]]]]]]]]]]]


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





2001-10-29