html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Power

 http://functions.wolfram.com/01.02.06.0036.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["f", "[", "z", "]"]], "a"], "\[Equal]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "\[Pi]", " ", RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List["Arg", "[", RowBox[List["f", "[", SubscriptBox["z", "0"], "]"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "-", RowBox[List[FractionBox["1", RowBox[List["2", " ", "\[Pi]"]]], RowBox[List["Arg", "[", FractionBox[RowBox[List["f", "[", "z", "]"]], RowBox[List["f", "[", SubscriptBox["z", "0"], "]"]]], "]"]]]]]], "]"]]]]], " ", "a", " ", SuperscriptBox[RowBox[List["f", "[", SubscriptBox["z", "0"], "]"]], "a"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[RowBox[List["Binomial", "[", RowBox[List[RowBox[List["k", "-", "a"]], ",", "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["a", "-", "j"]]], SubscriptBox["p", RowBox[List["j", ",", "k"]]], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "k"]]]]]]]]]]]]], "/;", RowBox[List[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[RowBox[List["f", "[", SubscriptBox["z", "0"], "]"]], "k"]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", "1"]], "k"], RowBox[List[FractionBox[RowBox[List[RowBox[List["j", " ", "m"]], "-", "k", "+", "m"]], RowBox[List["m", "!"]]], RowBox[List[SuperscriptBox["f", TagBox[RowBox[List["(", "m", ")"]], Derivative], Rule[MultilineFunction, None]], "[", SubscriptBox["z", "0"], "]"]], " ", SubscriptBox["p", RowBox[List["j", ",", RowBox[List["k", "-", "m"]]]]]]]]]]]]], "\[And]", RowBox[List["k", "\[Element]", "Integers"]], "\[And]", RowBox[List["k", ">", "0"]], "\[And]", RowBox[List[RowBox[List["f", "[", SubscriptBox["z", "0"], "]"]], "\[NotEqual]", "0"]]]]]]]]

 MathML Form

 f ( z ) a a f ( z 0 ) a 2 a π 1 2 - arg ( f ( z 0 ) ) 2 π - 1 2 π arg ( f ( z ) f ( z 0 ) ) k = 0 ( k - a k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox[RowBox[List["k", "-", "a"]], 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 a - 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 - z 0 ) k /; p j , 0 1 p j , k 1 f ( z 0 ) k m = 1 k j m + m - k m ! f ( m ) TagBox[RowBox[List["(", "m", ")"]], Derivative] ( z 0 ) p j , k - m k + f ( z 0 ) 0 Condition f z a a f Subscript z 0 a 2 a 1 2 -1 f Subscript z 0 2 -1 -1 1 2 -1 f z f Subscript z 0 -1 k 0 Binomial k -1 a k j 0 k -1 j a -1 j -1 Binomial k j Subscript p j k z -1 Subscript z 0 k Subscript p j 0 1 Subscript p j k 1 f Subscript z 0 k -1 m 1 k j m m -1 k m -1 D f Subscript z 0 Subscript z 0 m Subscript p j k -1 m k SuperPlus f Subscript z 0 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["f", "[", "z_", "]"]], "a_"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "\[Pi]", " ", RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List["Arg", "[", RowBox[List["f", "[", SubscriptBox["zz", "0"], "]"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "-", FractionBox[RowBox[List["Arg", "[", FractionBox[RowBox[List["f", "[", "z", "]"]], RowBox[List["f", "[", SubscriptBox["zz", "0"], "]"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]]]]], " ", "a", " ", SuperscriptBox[RowBox[List["f", "[", SubscriptBox["zz", "0"], "]"]], "a"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[RowBox[List["Binomial", "[", RowBox[List[RowBox[List["k", "-", "a"]], ",", "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[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]], "k"]]], RowBox[List["a", "-", "j"]]]]]]]]]]], "/;", RowBox[List[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"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["j", " ", "m"]], "-", "k", "+", "m"]], ")"]], " ", RowBox[List[SuperscriptBox["f", TagBox[RowBox[List["(", "m", ")"]], Derivative], Rule[MultilineFunction, None]], "[", SubscriptBox["zz", "0"], "]"]], " ", SubscriptBox["p", RowBox[List["j", ",", RowBox[List["k", "-", "m"]]]]]]], RowBox[List["m", "!"]]]]], RowBox[List[RowBox[List["f", "[", SubscriptBox["zz", "0"], "]"]], " ", "k"]]]]], "&&", RowBox[List["k", "\[Element]", "Integers"]], "&&", RowBox[List["k", ">", "0"]], "&&", RowBox[List[RowBox[List["f", "[", SubscriptBox["zz", "0"], "]"]], "\[NotEqual]", "0"]]]]]]]]]]

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

 2007-05-02