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 Exp

 http://functions.wolfram.com/01.03.06.0019.01

 Input Form

 E^z == Sum[(z^(2 k) (z + 2 k + 1))/(2 k + 1)!, {k, 0, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["2", "k"]]], RowBox[List["(", RowBox[List["z", "+", RowBox[List["2", "k"]], "+", "1"]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", "k"]], "+", "1"]], ")"]], "!"]]]]]]]]]

 MathML Form

 z k = 0 z 2 k ( z + 2 k + 1 ) ( 2 k + 1 ) ! z k 0 z 2 k z 2 k 1 2 k 1 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["\[ExponentialE]", "z_"], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["2", " ", "k"]]], " ", RowBox[List["(", RowBox[List["z", "+", RowBox[List["2", " ", "k"]], "+", "1"]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], "!"]]]]]]]]]

 Contributed by

 H. J. Brothers

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

 2003-08-21