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; }

 ArcSec

 http://functions.wolfram.com/01.18.16.0203.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["a_", " ", RowBox[List["ArcSec", "[", "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[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "x"]]], ")"]], 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