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variants of this functions
Log






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.04.16.0151.01









  


  










Input Form





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










Standard Form





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MathML Form







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<ci> a </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <arg /> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> <apply> <power /> <ci> x </ci> <ci> a </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <floor /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <arg /> <apply> <times /> <apply> <power /> <ci> x </ci> <ci> a </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <arccos /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <ci> x </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> b </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> b </ci> </apply> </apply> <apply> <power /> <ci> x </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </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





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