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ArcCosh






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.26.16.0225.01









  


  










Input Form





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










Standard Form





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MathML Form







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<imaginaryi /> <apply> <power /> <ci> y </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> b </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02