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 ArcCos

 http://functions.wolfram.com/01.13.16.0216.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["a_", " ", RowBox[List["ArcCos", "[", "x_", "]"]]]], "+", RowBox[List["b_", " ", RowBox[List["ArcCosh", "[", "y_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "a"]], "2"], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["-", RowBox[List["Arg", "[", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "x"]], "+", SqrtBox[RowBox[List["1", "-", SuperscriptBox["x", "2"]]]]]], ")"]], RowBox[List["\[ImaginaryI]", " ", "a"]]], "]"]]]], "-", RowBox[List["Arg", "[", SuperscriptBox[RowBox[List["(", RowBox[List["y", "+", RowBox[List[SqrtBox[RowBox[List["y", "-", "1"]]], " ", SqrtBox[RowBox[List["y", "+", "1"]]]]]]], ")"]], "b"], "]"]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02