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; }

 ArcSinh

 http://functions.wolfram.com/01.25.16.0142.01

 Input Form

 ArcSinh[x] + Log[y] == (-1)^(Floor[1/2 - Arg[(x + Sqrt[x^2 + 1]) y]/Pi] - Floor[-(Arg[(-I) (x + Sqrt[x^2 + 1]) y - 1]/(2 Pi)) - Arg[I (x + Sqrt[x^2 + 1]) y - 1]/(2 Pi) + 1/2]) ArcSinh[((x + Sqrt[x^2 + 1])^2 y^2 - 1)/(2 (x + Sqrt[x^2 + 1]) y)] - (1/2) I (-1)^(-Floor[-(Arg[(x + Sqrt[x^2 + 1]) y]/Pi)] - Floor[-(Arg[(-I) (x + Sqrt[x^2 + 1]) y - 1]/(2 Pi)) - Arg[I (x + Sqrt[x^2 + 1]) y - 1]/(2 Pi) + 1/2]) (1 - (-1)^Floor[1/2 - Arg[(x + Sqrt[x^2 + 1]) y]/Pi] + (-1)^(Floor[-(Arg[(x + Sqrt[x^2 + 1]) y]/Pi)] + Floor[-(Arg[(-I) (x + Sqrt[x^2 + 1]) y - 1]/(2 Pi)) - Arg[I (x + Sqrt[x^2 + 1]) y - 1]/(2 Pi) + 1/2] + Floor[Arg[(x + Sqrt[x^2 + 1]) y]/(2 Pi) - Arg[(x + Sqrt[x^2 + 1]) y - I]/(2 Pi) + 1/2] + Floor[-(Arg[(x + Sqrt[x^2 + 1]) y]/(2 Pi)) + Arg[(x + Sqrt[x^2 + 1]) y - I]/(2 Pi) + 1/2]) - (-1)^(Floor[-(Arg[(x + Sqrt[x^2 + 1]) y]/Pi)] + Floor[-(Arg[(-I) (x + Sqrt[x^2 + 1]) y - 1]/(2 Pi)) - Arg[I (x + Sqrt[x^2 + 1]) y - 1]/(2 Pi) + 1/2] + Floor[Arg[(x + Sqrt[x^2 + 1]) y]/(2 Pi) - Arg[(x + Sqrt[x^2 + 1]) y + I]/(2 Pi) + 1/2] + Floor[-(Arg[(x + Sqrt[x^2 + 1]) y]/(2 Pi)) + Arg[(x + Sqrt[x^2 + 1]) y + I]/(2 Pi) + 1/2])) Pi - 2 I Pi Floor[(-Arg[x + Sqrt[x^2 + 1]] - Arg[y] + Pi)/(2 Pi)]

 Standard Form

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

 MathML Form

 sinh - 1 ( x ) + log ( y ) ( - 1 ) 1 2 - arg ( ( x + x 2 + 1 ) y ) π - - arg ( ( x + x 2 + 1 ) ( - ) y - 1 ) 2 π + 1 2 - arg ( ( x + x 2 + 1 ) y - 1 ) 2 π sinh - 1 ( ( x + x 2 + 1 ) 2 y 2 - 1 2 ( x + x 2 + 1 ) y ) - 1 2 ( - 1 ) - - arg ( ( x + x 2 + 1 ) ( - ) y - 1 ) 2 π + 1 2 - arg ( ( x + x 2 + 1 ) y - 1 ) 2 π - - arg ( ( x + x 2 + 1 ) y ) π ( 1 - ( - 1 ) 1 2 - arg ( ( x + x 2 + 1 ) y ) π + ( - 1 ) arg ( ( x + x 2 + 1 ) y - ) 2 π + 1 2 - arg ( ( x + x 2 + 1 ) y ) 2 π + - arg ( ( x + x 2 + 1 ) ( - ) y - 1 ) 2 π + 1 2 - arg ( ( x + x 2 + 1 ) y - 1 ) 2 π + - arg ( ( x + x 2 + 1 ) y - ) 2 π + arg ( ( x + x 2 + 1 ) y ) 2 π + 1 2 + - arg ( ( x + x 2 + 1 ) y ) π - ( - 1 ) arg ( ( x + x 2 + 1 ) y + ) 2 π + 1 2 - arg ( ( x + x 2 + 1 ) y ) 2 π + - arg ( ( x + x 2 + 1 ) ( - ) y - 1 ) 2 π + 1 2 - arg ( ( x + x 2 + 1 ) y - 1 ) 2 π + - arg ( ( x + x 2 + 1 ) y + ) 2 π + arg ( ( x + x 2 + 1 ) y ) 2 π + 1 2 + - arg ( ( x + x 2 + 1 ) y ) π ) π - 2 π - arg ( x + x 2 + 1 ) - arg ( y ) + π 2 π x y -1 1 2 -1 x x 2 1 1 2 y -1 -1 -1 x x 2 1 1 2 -1 y -1 2 -1 1 2 -1 x x 2 1 1 2 y -1 2 -1 x x 2 1 1 2 2 y 2 -1 2 x x 2 1 1 2 y -1 -1 1 2 -1 -1 -1 x x 2 1 1 2 -1 y -1 2 -1 1 2 -1 x x 2 1 1 2 y -1 2 -1 -1 -1 x x 2 1 1 2 y -1 1 -1 -1 1 2 -1 x x 2 1 1 2 y -1 -1 x x 2 1 1 2 y -1 2 -1 1 2 -1 x x 2 1 1 2 y 2 -1 -1 x x 2 1 1 2 -1 y -1 2 -1 1 2 -1 x x 2 1 1 2 y -1 2 -1 -1 x x 2 1 1 2 y -1 2 -1 x x 2 1 1 2 y 2 -1 1 2 -1 x x 2 1 1 2 y -1 -1 -1 x x 2 1 1 2 y 2 -1 1 2 -1 x x 2 1 1 2 y 2 -1 -1 x x 2 1 1 2 -1 y -1 2 -1 1 2 -1 x x 2 1 1 2 y -1 2 -1 -1 x x 2 1 1 2 y 2 -1 x x 2 1 1 2 y 2 -1 1 2 -1 x x 2 1 1 2 y -1 -1 2 -1 x x 2 1 1 2 -1 y 2 -1 [/itex]

 Rule Form

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

 2007-05-02

© 1998-2013 Wolfram Research, Inc.