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Fungrim entry: 686ce0

θ4 ⁣(2z,2τ)=θ3 ⁣(z,τ)θ4 ⁣(z,τ)θ4 ⁣(0,2τ)\theta_{4}\!\left(2 z , 2 \tau\right) = \frac{\theta_{3}\!\left(z , \tau\right) \theta_{4}\!\left(z , \tau\right)}{\theta_{4}\!\left(0 , 2 \tau\right)}
Assumptions:zCandτHz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}
TeX:
\theta_{4}\!\left(2 z , 2 \tau\right) = \frac{\theta_{3}\!\left(z , \tau\right) \theta_{4}\!\left(z , \tau\right)}{\theta_{4}\!\left(0 , 2 \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("686ce0"),
    Formula(Equal(JacobiTheta(4, Mul(2, z), Mul(2, tau)), Div(Mul(JacobiTheta(3, z, tau), JacobiTheta(4, z, tau)), JacobiTheta(4, 0, Mul(2, tau))))),
    Variables(z, tau),
    Assumptions(And(Element(z, CC), Element(tau, HH))))

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2019-10-05 13:11:19.856591 UTC