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Fungrim entry: 5fe58d

θ1 ⁣(2z,τ)=2θ1 ⁣(z,τ)θ2 ⁣(z,τ)θ3 ⁣(z,τ)θ4 ⁣(z,τ)θ2 ⁣(0,τ)θ3 ⁣(0,τ)θ4 ⁣(0,τ)\theta_{1}\!\left(2 z , \tau\right) = \frac{2 \theta_{1}\!\left(z , \tau\right) \theta_{2}\!\left(z , \tau\right) \theta_{3}\!\left(z , \tau\right) \theta_{4}\!\left(z , \tau\right)}{\theta_{2}\!\left(0 , \tau\right) \theta_{3}\!\left(0 , \tau\right) \theta_{4}\!\left(0 , \tau\right)}
Assumptions:zC  and  τHz \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}
TeX:
\theta_{1}\!\left(2 z , \tau\right) = \frac{2 \theta_{1}\!\left(z , \tau\right) \theta_{2}\!\left(z , \tau\right) \theta_{3}\!\left(z , \tau\right) \theta_{4}\!\left(z , \tau\right)}{\theta_{2}\!\left(0 , \tau\right) \theta_{3}\!\left(0 , \tau\right) \theta_{4}\!\left(0 , \tau\right)}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
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("5fe58d"),
    Formula(Equal(JacobiTheta(1, Mul(2, z), tau), Div(Mul(Mul(Mul(Mul(2, JacobiTheta(1, z, tau)), JacobiTheta(2, z, tau)), JacobiTheta(3, z, tau)), JacobiTheta(4, z, tau)), Mul(Mul(JacobiTheta(2, 0, tau), JacobiTheta(3, 0, tau)), JacobiTheta(4, 0, tau))))),
    Variables(z, tau),
    Assumptions(And(Element(z, CC), Element(tau, HH))))

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2021-03-15 19:12:00.328586 UTC