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 Power

 http://functions.wolfram.com/01.02.06.0016.01

 Input Form

 1/z == Sum[(-1)^k (z - 1)^k, {k, 0, Infinity}] /; Abs[z - 1] < 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[FractionBox["1", "z"], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], "k"]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["z", "-", "1"]], "]"]], "<", "1"]]]]]]

 MathML Form

 1 z k = 0 ( - 1 ) k ( z - 1 ) k /; "\[LeftBracketingBar]" z - 1 "\[RightBracketingBar]" < 1 Condition 1 z -1 k 0 -1 k z -1 k z -1 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox["1", "z_"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], "k"]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["z", "-", "1"]], "]"]], "<", "1"]]]]]]]]

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

 2001-10-29