Hyperbolic cosine integral: Specific values (formula 01.20.03.0064)

Cosh

$Mathematica Notation$

Elementary Functions

Specific values

Values at fixed points

http://functions.wolfram.com/01.20.03.0064.01

Input Form

Cosh[(4 Pi I)/5] == -((Sqrt[5] + 1)/4)

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Cosh", "[", FractionBox[RowBox[List["4", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "5"], "]"]], "\[Equal]", RowBox[List["-", FractionBox[RowBox[List[SqrtBox["5"], "+", "1"]], "4"]]]]]]]

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> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> <mn> 5 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <msqrt> <mn> 5 </mn> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <cosh /> <apply> <times /> <cn type='integer'> 4 </cn> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cosh", "[", FractionBox[RowBox[List["4", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "5"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", RowBox[List["(", RowBox[List[SqrtBox["5"], "+", "1"]], ")"]]]]]]]]

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

2001-10-29