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/01.30.16.0242.01

 Input Form

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

 Standard Form

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

 Rule Form

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

 2007-05-02