KleinInvariantJ

Available

Normalized elliptic modular invariant J(tau) equal to j(tau)/1728 (exact at tau=I; numeric via theta ratio)

Forms

KleinInvariantJ[τ]

Verified examplesKleinInvariantJ[1 + 2.I]//Chop → 166.3749999999999 Plot[Re[KleinInvariantJ[x + I]], {x, -2, 2}] → -Graphics-Series[KleinInvariantJ[x + I], {x, 0, 3}]//Normal//FullSimplify → 1 + x*Derivative[1][KleinInvariantJ][I] + (x^2*Derivative[2][KleinInvariantJ][I])/2 + (x^3*Derivative[3][KleinInvariantJ][I])/6

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Topics

Q Functions - Related Functions
Special Functions - Modular Forms

Related

ModularLambda DedekindEta WeierstrassInvariants EllipticTheta InverseEllipticNomeQ

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