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 Log

 http://functions.wolfram.com/01.04.16.0155.01

 Input Form

 a Log[x] + b ArcCot[y] == -2 I Pi (Floor[(-Arg[x^a] - Arg[(1 - I/y)^((I b)/2)] + Pi)/(2 Pi)] + Floor[(Pi - Im[a Log[x]])/(2 Pi)] + Floor[(Pi - (1/2) Re[b Log[1 - I/y]])/ (2 Pi)]) - 2 I Pi (Floor[(-Arg[x^a (1 - I/y)^((I b)/2)] - Arg[(1 + I/y)^((-(1/2)) (I b))] + Pi)/(2 Pi)] + Floor[(Pi - Im[Log[x^a (1 - I/y)^((I b)/2)]])/(2 Pi)] + Floor[((1/2) Re[b Log[1 + I/y]] + Pi)/(2 Pi)]) + I Pi (1 - (-1)^Floor[Arg[((1 - I/y)^((I b)/2) x^a)/(1 + I/y)^((1/2) (I b)) + 1]/ (2 Pi) + 1/2]) + 2 I ArcCot[(I (((1 - I/y)^((I b)/2) x^a)/(1 + I/y)^((1/2) (I b)) + 1))/ ((x^a (1 - I/y)^((I b)/2))/(1 + I/y)^((1/2) (I b)) - 1)]

 Standard Form

 Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List[RowBox[List["a", " ", RowBox[List["Log", "[", "x", "]"]]]], "+", RowBox[List["b", " ", RowBox[List["ArcCot", "[", "y", "]"]]]]]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["-", RowBox[List["Arg", "[", SuperscriptBox["x", "a"], "]"]]]], "-", RowBox[List["Arg", "[", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", FractionBox["\[ImaginaryI]", "y"]]], ")"]], FractionBox[RowBox[List["\[ImaginaryI]", " ", "b"]], "2"]], "]"]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "x", "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Re", "[", RowBox[List["b", " ", RowBox[List["Log", "[", RowBox[List["1", "-", FractionBox["\[ImaginaryI]", "y"]]], "]"]]]], "]"]]]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], ")"]]]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["-", RowBox[List["Arg", "[", RowBox[List[SuperscriptBox["x", "a"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", FractionBox["\[ImaginaryI]", "y"]]], ")"]], FractionBox[RowBox[List["\[ImaginaryI]", " ", "b"]], "2"]]]], "]"]]]], "-", RowBox[List["Arg", "[", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox["\[ImaginaryI]", "y"]]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]]]]], "]"]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", RowBox[List["Log", "[", RowBox[List[SuperscriptBox["x", "a"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", FractionBox["\[ImaginaryI]", "y"]]], ")"]], FractionBox[RowBox[List["\[ImaginaryI]", " ", "b"]], "2"]]]], "]"]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Re", "[", RowBox[List["b", " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox["\[ImaginaryI]", "y"]]], "]"]]]], "]"]]]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], ")"]]]], "+", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Floor", "[", RowBox[List[FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", FractionBox["\[ImaginaryI]", "y"]]], ")"]], FractionBox[RowBox[List["\[ImaginaryI]", " ", "b"]], "2"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox["\[ImaginaryI]", "y"]]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]]]]], " ", SuperscriptBox["x", "a"]]], "+", "1"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "+", FractionBox["1", "2"]]], "]"]]]]], ")"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["ArcCot", "[", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", FractionBox["\[ImaginaryI]", "y"]]], ")"]], FractionBox[RowBox[List["\[ImaginaryI]", " ", "b"]], "2"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox["\[ImaginaryI]", "y"]]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]]]]], " ", SuperscriptBox["x", "a"]]], "+", "1"]], ")"]]]], RowBox[List[RowBox[List[SuperscriptBox["x", "a"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", FractionBox["\[ImaginaryI]", "y"]]], ")"]], FractionBox[RowBox[List["\[ImaginaryI]", " ", "b"]], "2"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox["\[ImaginaryI]", "y"]]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]]]]]]], "-", "1"]]], "]"]]]]]]]]]]]]

 MathML Form

 a log ( x ) + b cot - 1 ( y ) - 2 π ( - arg ( ( 1 + y ) - 1 2 ( b ) ) - arg ( x a ( 1 - y ) b 2 ) + π 2 π + 1 2 Re ( b log ( 1 + y ) ) + π 2 π + π - Im ( log ( x a ( 1 - y ) b 2 ) ) 2 π ) - 2 π ( - arg ( x a ) - arg ( ( 1 - y ) b 2 ) + π 2 π + π - Im ( a log ( x ) ) 2 π + π - 1 2 Re ( b log ( 1 - y ) ) 2 π ) + π ( 1 - ( - 1 ) arg ( x a ( 1 + y ) - 1 2 ( b ) ( 1 - y ) b 2 + 1 ) 2 π + 1 2 ) + 2 cot - 1 ( ( x a ( 1 + y ) - 1 2 ( b ) ( 1 - y ) b 2 + 1 ) x a ( 1 - y ) b 2 ( 1 + y ) - 1 2 ( b ) - 1 ) a x b y -2 -1 1 y -1 -1 1 2 b -1 x a 1 -1 y -1 b 2 -1 2 -1 1 2 b 1 y -1 2 -1 -1 x a 1 -1 y -1 b 2 -1 2 -1 -1 2 -1 x a -1 1 -1 y -1 b 2 -1 2 -1 -1 a x 2 -1 -1 1 2 b 1 -1 y -1 2 -1 1 -1 -1 x a 1 y -1 -1 1 2 b 1 -1 y -1 b 2 -1 1 2 -1 1 2 2 x a 1 y -1 -1 1 2 b 1 -1 y -1 b 2 -1 1 x a 1 -1 y -1 b 2 -1 1 y -1 -1 1 2 b -1 -1 [/itex]

 Rule Form

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

 2007-05-02