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Sech




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.24.16.0041.01









  


  








Input Form





Sech[a]^2 + Csch[b]^2 == Cosh[a - b] Cosh[a + b] Csch[b]^2 Sech[a]^2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["Sech", "[", "a", "]"]], "2"], "+", SuperscriptBox[RowBox[List["Csch", "[", "b", "]"]], "2"]]], "\[Equal]", RowBox[List[RowBox[List["Cosh", "[", RowBox[List["a", "-", "b"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["a", "+", "b"]], "]"]], " ", SuperscriptBox[RowBox[List["Csch", "[", "b", "]"]], "2"], " ", SuperscriptBox[RowBox[List["Sech", "[", "a", "]"]], "2"]]]]]]]








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> <msup> <mi> csch </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msup> <mi> sech </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> csch </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> sech </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <power /> <apply> <csch /> <ci> b </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <sech /> <ci> a </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <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> <power /> <apply> <csch /> <ci> b </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <sech /> <ci> a </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox[RowBox[List["Sech", "[", "a_", "]"]], "2"], "+", SuperscriptBox[RowBox[List["Csch", "[", "b_", "]"]], "2"]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Cosh", "[", RowBox[List["a", "-", "b"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["a", "+", "b"]], "]"]], " ", SuperscriptBox[RowBox[List["Csch", "[", "b", "]"]], "2"], " ", SuperscriptBox[RowBox[List["Sech", "[", "a", "]"]], "2"]]]]]]]


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





2001-10-29