Exponential function: Specific values (formula 01.03.03.0186)

Exp

$Mathematica Notation$

Elementary Functions

Specific values

Values at fixed points

http://functions.wolfram.com/01.03.03.0186.01

Input Form

E^((9 Pi I)/5) == (1 + Sqrt[5])/4 - (I/2) Sqrt[(5 - Sqrt[5])/2]

Standard Form

Cell[BoxData[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["9", "\[Pi]", " ", "\[ImaginaryI]"]], "5"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["1", "+", SqrtBox["5"]]], "4"], "-", RowBox[List[FractionBox["\[ImaginaryI]", "2"], SqrtBox[FractionBox[RowBox[List["5", "-", SqrtBox["5"]]], "2"]]]]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msup> <mi> ⅇ </mi> <mfrac> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> <mn> 5 </mn> </mfrac> </msup> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <mn> 1 </mn> <mo> + </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> <mn> 4 </mn> </mfrac> <mo> - </mo> <mrow> <mfrac> <mi> ⅈ </mi> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <msqrt> <mfrac> <mrow> <mn> 5 </mn> <mo> - </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> <mn> 2 </mn> </mfrac> </msqrt> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 9 </cn> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["9", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "5"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["5"]]], ")"]]]], "-", RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["5", "-", SqrtBox["5"]]], ")"]]]]]]]]]]]]]

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

2001-10-29