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; }

 ArcSin

 http://functions.wolfram.com/01.12.16.0218.01

 Input Form

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

 Standard Form

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SqrtBox[RowBox[List["1", "-", SuperscriptBox["x", "2"]]]]]], "]"]]]], "]"]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], ")"]]]]]]]]]]]]

 MathML Form

 a sin - 1 ( x ) + b sech - 1 ( y ) π ( 1 - ( - 1 ) - arg ( ( 1 y - 1 1 + 1 y + 1 y ) b ( x + 1 - x 2 ) - a + 1 ) 2 π - - arg ( ( x + 1 - x 2 ) - a ( 1 y - 1 1 + 1 y + 1 y ) b ) 2 π ) + ( - 1 ) arg ( ( x + 1 - x 2 ) - a ( 1 y - 1 1 + 1 y + 1 y ) b ) π - 2 arg ( ( x + 1 - x 2 ) - a ( 1 y - 1 1 + 1 y + 1 y ) b - 1 ) π + - arg ( ( x + 1 - x 2 ) - a ( 1 y - 1 1 + 1 y + 1 y ) b ) π - - arg ( ( x + 1 - x 2 ) - a ( 1 y - 1 1 + 1 y + 1 y ) b - 1 ) 2 π + - arg ( ( 1 y - 1 1 + 1 y + 1 y ) b ( x + 1 - x 2 ) - a + 1 ) 2 π sech - 1 ( 2 ( x + 1 - x 2 ) - a ( 1 y - 1 1 + 1 y + 1 y ) b ( 1 y - 1 1 + 1 y + 1 y ) 2 b ( x + 1 - x 2 ) - 2 a + 1 ) - 2 π ( - arg ( ( x + 1 - x 2 ) - a ) - arg ( ( 1 y - 1 1 + 1 y + 1 y ) b ) + π 2 π + Re ( a log ( x + 1 - x 2 ) ) + π 2 π + π - Im ( b log ( 1 y - 1 1 + 1 y + 1 y ) ) 2 π ) a x b y 1 -1 -1 -1 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 b x 1 -1 x 2 1 2 -1 a 1 2 -1 -1 -1 x 1 -1 x 2 1 2 -1 a 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 b 2 -1 -1 x 1 -1 x 2 1 2 -1 a 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 b -1 -1 2 x 1 -1 x 2 1 2 -1 a 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 b -1 -1 -1 x 1 -1 x 2 1 2 -1 a 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 b -1 -1 -1 x 1 -1 x 2 1 2 -1 a 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 b -1 2 -1 -1 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 b x 1 -1 x 2 1 2 -1 a 1 2 -1 2 x 1 -1 x 2 1 2 -1 a 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 b 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 2 b x 1 -1 x 2 1 2 -2 a 1 -1 -1 2 -1 x 1 -1 x 2 1 2 -1 a -1 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 b 2 -1 a x 1 -1 x 2 1 2 2 -1 -1 b 1 y -1 -1 1 2 1 1 y -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