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 Power

 http://functions.wolfram.com/01.02.06.0024.01

 Input Form

 z^a == z^Subscript[a, 0] Sum[(Log[z]^k/k!) (a - Subscript[a, 0])^k, {k, 0, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List[SuperscriptBox["z", "a"], "\[Equal]", RowBox[List[SuperscriptBox["z", SubscriptBox["a", "0"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox[SuperscriptBox[RowBox[List["Log", "[", "z", "]"]], "k"], RowBox[List["k", "!"]]], SuperscriptBox[RowBox[List["(", RowBox[List["a", "-", SubscriptBox["a", "0"]]], ")"]], "k"]]]]]]]]]]]

 MathML Form

 z a z a 0 k = 0 log k ( z ) k ! ( a - a 0 ) k z a z Subscript a 0 k 0 z k k -1 a -1 Subscript a 0 k [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["z_", "a_"], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["z", SubscriptBox["aa", "0"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["Log", "[", "z", "]"]], "k"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "-", SubscriptBox["aa", "0"]]], ")"]], "k"]]], RowBox[List["k", "!"]]]]]]]]]]]

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

 2007-05-02