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DedekindEta






Mathematica Notation

Traditional Notation









Elliptic Functions > DedekindEta[z] > Differentiation > Low-order differentiation





http://functions.wolfram.com/09.49.20.0001.02









  


  










Input Form





D[DedekindEta[z], z] == -4096 I EllipticK[ModularLambda[z]]^13 ((-81 EllipticE[ModularLambda[z]] (-1 + KleinInvariantJ[z]) KleinInvariantJ[z] (-2 + ModularLambda[z])^6 (-1 + ModularLambda[z])^2 ModularLambda[z]^2 (1 + ModularLambda[z])^6 (-1 + 2 ModularLambda[z])^6 (1 - ModularLambda[z] + ModularLambda[z]^2)^12 + EllipticK[ModularLambda[z]] (1 - ModularLambda[z] + ModularLambda[z]^2)^ 11 (2 - 3 ModularLambda[z] - 3 ModularLambda[z]^2 + 2 ModularLambda[z]^3)^5 (-2 (-4 + 7 KleinInvariantJ[z]) (1 - 2 ModularLambda[z])^2 (-2 + ModularLambda[z])^2 (1 + ModularLambda[z])^2 (1 + (-1 + ModularLambda[z]) ModularLambda[z])^3 + 81 (-1 + KleinInvariantJ[z]) KleinInvariantJ[z] (-1 + ModularLambda[z])^2 ModularLambda[z]^2 (6 - 18 ModularLambda[z] + 13 ModularLambda[z]^2 + 4 ModularLambda[z]^3 + 6 ModularLambda[z]^4 - 11 ModularLambda[z]^5 + 4 ModularLambda[z]^6)))/(847288609443 Pi^13 DedekindEta[z]^23 (-1 + KleinInvariantJ[z])^4 KleinInvariantJ[z]^5 (-1 + ModularLambda[z])^14 ModularLambda[z]^14))










Standard Form





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MathML Form







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Rule Form





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





2001-10-29





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