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; }

 Log

 http://functions.wolfram.com/01.04.16.0169.01

 Input Form

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

 Standard Form

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")"]]]]]]]]]]]]

 MathML Form

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

 Rule Form

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

 2007-05-02