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ModularLambda

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Elliptic modular lambda function lambda(tau) equal to (theta2/theta3)^4 (exact at tau=I; numeric in the upper half-plane)

ModularLambda[τ]
ModularLambda[1 + 3.I] → -0.001292026239994776 + 4.336808689942018*^-19*IPlot[Re[ModularLambda[x + I]], {x, -2, 2}] → -Graphics-Series[ModularLambda[x + I], {x, 0, 3}]//Normal//FullSimplify → x*Derivative[1][ModularLambda][I] + (1 + x^2*Derivative[2][ModularLambda][I])/2 + (x^3*Derivative[3][ModularLambda][I])/6
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Correlate

DedekindEtaKleinInvariantJWeierstrassHalfPeriodsEllipticThetaInverseEllipticNomeQ

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