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Fungrim entry: 265d9c

θ22 ⁣(0,τ)θ42 ⁣(z,τ)=θ32 ⁣(0,τ)θ12 ⁣(z,τ)+θ42 ⁣(0,τ)θ22 ⁣(z,τ)\theta_{2}^{2}\!\left(0, \tau\right) \theta_{4}^{2}\!\left(z, \tau\right) = \theta_{3}^{2}\!\left(0, \tau\right) \theta_{1}^{2}\!\left(z, \tau\right) + \theta_{4}^{2}\!\left(0, \tau\right) \theta_{2}^{2}\!\left(z, \tau\right)
Assumptions:zCandτHz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}
TeX:
\theta_{2}^{2}\!\left(0, \tau\right) \theta_{4}^{2}\!\left(z, \tau\right) = \theta_{3}^{2}\!\left(0, \tau\right) \theta_{1}^{2}\!\left(z, \tau\right) + \theta_{4}^{2}\!\left(0, \tau\right) \theta_{2}^{2}\!\left(z, \tau\right)

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("265d9c"),
    Formula(Equal(Mul(Pow(JacobiTheta(2, 0, tau), 2), Pow(JacobiTheta(4, z, tau), 2)), Add(Mul(Pow(JacobiTheta(3, 0, tau), 2), Pow(JacobiTheta(1, z, tau), 2)), Mul(Pow(JacobiTheta(4, 0, tau), 2), Pow(JacobiTheta(2, z, tau), 2))))),
    Variables(z, tau),
    Assumptions(And(Element(z, CC), Element(tau, HH))))

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2019-09-20 18:07:53.062439 UTC