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ModularLambda






Mathematica Notation

Traditional Notation









Elliptic Functions > ModularLambda[z] > Series representations > Generalized power series > Expansions at z==0





http://functions.wolfram.com/09.51.06.0003.01









  


  










Input Form





ModularLambda[z] \[Proportional] 1 - 16/E^((I Pi)/z) + 128/E^((2 I Pi)/z) - 704/E^((3 I Pi)/z) + 3072/E^((4 I Pi)/z) - 11488/E^((5 I Pi)/z) + 38400/E^((6 I Pi)/z) - 117632/E^((7 I Pi)/z) + 335872/E^((8 I Pi)/z) - 904784/E^((9 I Pi)/z) + 2320128/E^((10 I Pi)/z) - 5702208/E^((11 I Pi)/z) + 13504512/E^((12 I Pi)/z) - 30952544/E^((13 I Pi)/z) + 68901888/E^((14 I Pi)/z) - 149403264/E^((15 I Pi)/z) + 316342272/E^((16 I Pi)/z) - 655445792/E^((17 I Pi)/z) + 1331327616/E^((18 I Pi)/z) - 2655115712/E^((19 I Pi)/z) + 5206288384/E^((20 I Pi)/z) + O[E^(-((21 I Pi)/z))] /; Im[z] > 0 && (z -> 0)










Standard Form





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MathML Form







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</ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5206288384 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 20 </cn> <imaginaryi /> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 21 </cn> <imaginaryi /> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <gt /> <apply> <imaginary /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <cn type='integer'> 0 </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





© 1998- Wolfram Research, Inc.