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ArcSec






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSec[z] > Series representations > Generalized power series > Expansions at generic point z==z0 > For the function itself





http://functions.wolfram.com/01.18.06.0021.01









  


  










Input Form





ArcSec[z] == (Subscript[z, 0]/(Subscript[z, 0] - 1))^ ((1/2) Floor[Arg[(z - Subscript[z, 0])/(z Subscript[z, 0])]/(2 Pi)]) ((Subscript[z, 0] - 1)/Subscript[z, 0])^ ((1/2) Floor[Arg[(z - Subscript[z, 0])/(z Subscript[z, 0])]/(2 Pi)]) (-2 Pi I I^Floor[Arg[(-z + Subscript[z, 0])/(z Subscript[z, 0])]/(2 Pi)] Floor[Arg[(-z + Subscript[z, 0])/(z Subscript[z, 0])]/(2 Pi)] Floor[(Pi + Arg[(Subscript[z, 0] + 1)/Subscript[z, 0]])/(2 Pi)] + (Subscript[z, 0]/(Subscript[z, 0] + 1))^ ((1/2) Floor[Arg[(-z + Subscript[z, 0])/(z Subscript[z, 0])]/(2 Pi)]) ((Subscript[z, 0] + 1)/Subscript[z, 0])^ ((1/2) Floor[Arg[(-z + Subscript[z, 0])/(z Subscript[z, 0])]/(2 Pi)]) (Pi/2 + Sum[(-1)^(k - 1) Subscript[z, 0]^(-k - 1) HypergeometricPFQ[{1/2, (1 + k)/2, 1 + k/2}, {1, 3/2}, 1/Subscript[z, 0]^2] (z - Subscript[z, 0])^k, {k, 0, Infinity}]))










Standard Form





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MathML Form







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<apply> <power /> <apply> <times /> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <floor /> <apply> <times /> <apply> <arg /> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> k </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <apply> <plus /> <ci> k </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> k </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </list> <list> <cn type='integer'> 1 </cn> <cn type='rational'> 3 <sep /> 2 </cn> </list> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <ci> k </ci> </apply> </apply> </apply> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <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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