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; }

 ArcSech

 http://functions.wolfram.com/01.30.16.0238.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

 2007-05-02