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Tanh




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.21.16.0043.01









  


  








Input Form





Tanh[a] Tanh[b] == (Cosh[a + b] - Cosh[a - b])/(Cosh[a - b] + Cosh[a + b])








Standard Form





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


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





2001-10-29