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ArcSin






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSin[z] > Transformations > Related transformations > Linear combinations involving the direct function > Involving sec-1(z)





http://functions.wolfram.com/01.12.16.0206.01









  


  










Input Form





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










Standard Form





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MathML Form







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Rule Form





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





2007-05-02