Exponential function: Identities (formula 01.03.17.0003)

Exp

$Mathematica Notation$

Elementary Functions

Exp[z]

Identities

Recurrence identities

Distant neighbors

http://functions.wolfram.com/01.03.17.0003.01

Input Form

E^z == (1/E^n) E^(z + n) /; Element[n, Integers]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "\[Equal]", RowBox[List[FractionBox["1", SuperscriptBox["\[ExponentialE]", "n"]], SuperscriptBox["\[ExponentialE]", RowBox[List["z", "+", "n"]]]]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mi> ⅇ </mi> <mi> n </mi> </msup> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> z </mi> <mo> + </mo> <mi> n </mi> </mrow> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> ∈ </mo> <mi> ℤ </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <exponentiale /> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <plus /> <ci> z </ci> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <ci> ℤ </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["\[ExponentialE]", "z_"], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List["z", "+", "n"]]], SuperscriptBox["\[ExponentialE]", "n"]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]]]

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

2001-10-29