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 Log

 http://functions.wolfram.com/01.04.06.0036.01

 Input Form

 (c Log[1 + z])^\[Alpha] == E^(2 I \[Alpha] Pi Floor[1/2 - Arg[c]/(2 Pi) - Arg[z]/(2 Pi) - (1/(2 Pi)) Arg[Log[1 + z]/e]]) c^\[Alpha] z^\[Alpha] \[Alpha] Sum[Binomial[k - \[Alpha], k] Sum[(((-1)^j Binomial[k, j])/(\[Alpha] - j)) Subscript[p, j, k] z^k, {j, 0, k}], {k, 0, Infinity}] /; c != 0 && Subscript[c, k] == (c (-1)^k)/(k + 1) && Subscript[p, j, 0] == 1 && Subscript[p, j, k] == (1/(c k)) Sum[(j m - k + m) Subscript[c, m] Subscript[p, j, k - m], {m, 1, k}] && Element[k, Integers] && k > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["c", " ", RowBox[List["Log", "[", RowBox[List["1", "+", "z"]], "]"]]]], ")"]], "\[Alpha]"], "\[Equal]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Alpha]", " ", "\[Pi]", " ", RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List["Arg", "[", "c", "]"]], RowBox[List["2", " ", "\[Pi]"]]], "-", FractionBox[RowBox[List["Arg", "[", "z", "]"]], RowBox[List["2", " ", "\[Pi]"]]], "-", RowBox[List[FractionBox["1", RowBox[List["2", " ", "\[Pi]"]]], RowBox[List["Arg", "[", FractionBox[RowBox[List["Log", "[", RowBox[List["1", "+", "z"]], "]"]], "e"], "]"]]]]]], "]"]]]]], SuperscriptBox["c", "\[Alpha]"], SuperscriptBox["z", "\[Alpha]"], "\[Alpha]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[RowBox[List["Binomial", "[", RowBox[List[RowBox[List["k", "-", "\[Alpha]"]], ",", "k"]], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "k"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], " ", RowBox[List["Binomial", "[", RowBox[List["k", ",", "j"]], "]"]]]], RowBox[List["\[Alpha]", "-", "j"]]], SubscriptBox["p", RowBox[List["j", ",", "k"]]], SuperscriptBox["z", "k"]]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["c", "\[NotEqual]", "0"]], "\[And]", RowBox[List[SubscriptBox["c", "k"], "\[Equal]", FractionBox[RowBox[List["c", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"]]], RowBox[List["k", "+", "1"]]]]], "\[And]", RowBox[List[SubscriptBox["p", RowBox[List["j", ",", "0"]]], "\[Equal]", "1"]], "\[And]", RowBox[List[SubscriptBox["p", RowBox[List["j", ",", "k"]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["c", " ", "k"]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", "1"]], "k"], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["j", " ", "m"]], "-", "k", "+", "m"]], ")"]], SubscriptBox["c", "m"], " ", SubscriptBox["p", RowBox[List["j", ",", RowBox[List["k", "-", "m"]]]]]]]]]]]]], "\[And]", RowBox[List["k", "\[Element]", "Integers"]], "\[And]", RowBox[List["k", ">", "0"]]]]]]]]

 MathML Form

 ( c log ( 1 + z ) ) α 2 α π - arg ( c ) 2 π - 1 2 π arg ( log ( z + 1 ) e ) + 1 2 - arg ( z ) 2 π c α z α α k = 0 ( k - α k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox[RowBox[List["k", "-", "\[Alpha]"]], Identity, Rule[Editable, True]]], List[TagBox["k", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] j = 0 k ( - 1 ) j α - j ( k j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["k", Identity, Rule[Editable, True]]], List[TagBox["j", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] p j , k z k /; c 0 c k c ( - 1 ) k k + 1 p j , 0 1 p j , k 1 c k m = 1 k ( j m - k + m ) c m p j , k - m k + Condition c 1 z α 2 α -1 c 2 -1 -1 1 2 -1 z 1 e -1 1 2 -1 z 2 -1 c α z α α k 0 Binomial k -1 α k j 0 k -1 j α -1 j -1 Binomial k j Subscript p j k z k c 0 Subscript c k c -1 k k 1 -1 Subscript p j 0 1 Subscript p j k 1 c k -1 m 1 k j m -1 k m Subscript c m Subscript p j k -1 m k SuperPlus [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["(", RowBox[List["c_", " ", RowBox[List["Log", "[", RowBox[List["1", "+", "z_"]], "]"]]]], ")"]], "\[Alpha]_"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Alpha]", " ", "\[Pi]", " ", RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List["Arg", "[", "c", "]"]], RowBox[List["2", " ", "\[Pi]"]]], "-", FractionBox[RowBox[List["Arg", "[", "z", "]"]], RowBox[List["2", " ", "\[Pi]"]]], "-", FractionBox[RowBox[List["Arg", "[", FractionBox[RowBox[List["Log", "[", RowBox[List["1", "+", "z"]], "]"]], "e"], "]"]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]]]]], " ", SuperscriptBox["c", "\[Alpha]"], " ", SuperscriptBox["z", "\[Alpha]"], " ", "\[Alpha]", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[RowBox[List["Binomial", "[", RowBox[List[RowBox[List["k", "-", "\[Alpha]"]], ",", "k"]], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "k"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], " ", RowBox[List["Binomial", "[", RowBox[List["k", ",", "j"]], "]"]]]], ")"]], " ", SubscriptBox["p", RowBox[List["j", ",", "k"]]], " ", SuperscriptBox["z", "k"]]], RowBox[List["\[Alpha]", "-", "j"]]]]]]]]]]], "/;", RowBox[List[RowBox[List["c", "\[NotEqual]", "0"]], "&&", RowBox[List[SubscriptBox["c", "k"], "\[Equal]", FractionBox[RowBox[List["c", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"]]], RowBox[List["k", "+", "1"]]]]], "&&", RowBox[List[SubscriptBox["p", RowBox[List["j", ",", "0"]]], "\[Equal]", "1"]], "&&", RowBox[List[SubscriptBox["p", RowBox[List["j", ",", "k"]]], "\[Equal]", FractionBox[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", "1"]], "k"], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["j", " ", "m"]], "-", "k", "+", "m"]], ")"]], " ", SubscriptBox["c", "m"], " ", SubscriptBox["p", RowBox[List["j", ",", RowBox[List["k", "-", "m"]]]]]]]]], RowBox[List["c", " ", "k"]]]]], "&&", RowBox[List["k", "\[Element]", "Integers"]], "&&", RowBox[List["k", ">", "0"]]]]]]]]]]

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

 2007-05-02