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Fungrim entry: ebc673

θj ⁣(z,τ)4πiddτθj ⁣(z,τ)=0\theta''_{j}\!\left(z , \tau\right) - 4 \pi i \frac{d}{d \tau}\, \theta_{j}\!\left(z , \tau\right) = 0
Assumptions:j{1,2,3,4}  and  zC  and  τHj \in \left\{1, 2, 3, 4\right\} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}
\theta''_{j}\!\left(z , \tau\right) - 4 \pi i \frac{d}{d \tau}\, \theta_{j}\!\left(z , \tau\right) = 0

j \in \left\{1, 2, 3, 4\right\} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}
Fungrim symbol Notation Short description
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
Piπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
    Formula(Equal(Sub(JacobiTheta(j, z, tau, 2), Mul(Mul(Mul(4, Pi), ConstI), ComplexDerivative(JacobiTheta(j, z, tau), For(tau, tau)))), 0)),
    Variables(j, z, tau),
    Assumptions(And(Element(j, Set(1, 2, 3, 4)), Element(z, CC), Element(tau, HH))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC