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Fungrim entry: abbe42

θ32 ⁣(0,τ)θ42 ⁣(z,τ)=θ22 ⁣(0,τ)θ12 ⁣(z,τ)+θ42 ⁣(0,τ)θ32 ⁣(z,τ)\theta_{3}^{2}\!\left(0, \tau\right) \theta_{4}^{2}\!\left(z, \tau\right) = \theta_{2}^{2}\!\left(0, \tau\right) \theta_{1}^{2}\!\left(z, \tau\right) + \theta_{4}^{2}\!\left(0, \tau\right) \theta_{3}^{2}\!\left(z, \tau\right)
Assumptions:zC  and  τHz \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}
TeX:
\theta_{3}^{2}\!\left(0, \tau\right) \theta_{4}^{2}\!\left(z, \tau\right) = \theta_{2}^{2}\!\left(0, \tau\right) \theta_{1}^{2}\!\left(z, \tau\right) + \theta_{4}^{2}\!\left(0, \tau\right) \theta_{3}^{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("abbe42"),
    Formula(Equal(Mul(Pow(JacobiTheta(3, 0, tau), 2), Pow(JacobiTheta(4, z, tau), 2)), Add(Mul(Pow(JacobiTheta(2, 0, tau), 2), Pow(JacobiTheta(1, z, tau), 2)), Mul(Pow(JacobiTheta(4, 0, tau), 2), Pow(JacobiTheta(3, z, tau), 2))))),
    Variables(z, tau),
    Assumptions(And(Element(z, CC), Element(tau, HH))))

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2021-03-15 19:12:00.328586 UTC