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KleinInvariantJ






Mathematica Notation

Traditional Notation









Elliptic Functions > KleinInvariantJ[z] > Representations through equivalent functions > With inverse function





http://functions.wolfram.com/09.50.27.0001.01









  


  










Input Form





z == (I (r - s))/(r + s) /; {r, s} == {Gamma[5/12]^2 Hypergeometric2F1[1/12, 1/12, 1/2, 1 - \[Lambda]], 2 (Sqrt[3] - 2) Gamma[11/12]^2 Sqrt[\[Lambda] - 1] Hypergeometric2F1[7/12, 7/12, 3/2, 1 - \[Lambda]]} && Abs[z] >= 1 && -(1/2) <= Re[z] <= 0 && \[Lambda] == KleinInvariantJ[z]










Standard Form





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MathML Form







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</ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 11 <sep /> 12 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Hypergeometric2F1 </ci> <cn type='rational'> 7 <sep /> 12 </cn> <cn type='rational'> 7 <sep /> 12 </cn> <cn type='rational'> 3 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#955; </ci> </apply> </apply> </apply> </apply> </list> </apply> <apply> <geq /> <apply> <abs /> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <leq /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <real /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <ci> &#955; </ci> <apply> <ci> KleinInvariantJ </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





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