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InverseEllipticNomeQ






Mathematica Notation

Traditional Notation









Elliptic Functions > InverseEllipticNomeQ[z] > Series representations > Generalized power series > Expansions at z==1





http://functions.wolfram.com/09.52.06.0006.01









  


  










Input Form





InverseEllipticNomeQ[z] \[Proportional] 1 - 16 E^(Pi^2/Log[z]) + 128 E^((2 Pi^2)/Log[z]) - 704 E^((3 Pi^2)/Log[z]) + 3072 E^((4 Pi^2)/Log[z]) - 11488 E^((5 Pi^2)/Log[z]) + 38400 E^((6 Pi^2)/Log[z]) - 117632 E^((7 Pi^2)/Log[z]) + 335872 E^((8 Pi^2)/Log[z]) - 904784 E^((9 Pi^2)/Log[z]) + 2320128 E^((10 Pi^2)/Log[z]) - 5702208 E^((11 Pi^2)/Log[z]) + 13504512 E^((12 Pi^2)/Log[z]) - 30952544 E^((13 Pi^2)/Log[z]) + 68901888 E^((14 Pi^2)/Log[z]) - 149403264 E^((15 Pi^2)/Log[z]) + 316342272 E^((16 Pi^2)/Log[z]) - 655445792 E^((17 Pi^2)/Log[z]) + 1331327616 E^((18 Pi^2)/Log[z]) - 2655115712 E^((19 Pi^2)/Log[z]) + 5206288384 E^((20 Pi^2)/Log[z]) + O[E^((21 Pi^2)/Log[z])] /; Abs[z] < 1 && (z -> 1)










Standard Form





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MathML Form







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/> <exponentiale /> <apply> <times /> <cn type='integer'> 14 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ln /> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 149403264 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ln /> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 316342272 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ln /> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 655445792 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 17 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ln /> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1331327616 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 18 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ln /> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2655115712 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 19 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ln /> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5206288384 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 20 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ln /> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 21 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ln /> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <lt /> <apply> <abs /> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </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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