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Fungrim entry: a891da

θj ⁣(z,τ)=θj ⁣(z,τ)\theta_{j}\!\left(\overline{z} , \tau\right) = \overline{\theta_{j}\!\left(z , -\overline{\tau}\right)}
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(\overline{z} , \tau\right) = \overline{\theta_{j}\!\left(z , -\overline{\tau}\right)}

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
Conjugatez\overline{z} Complex conjugate
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
    Formula(Equal(JacobiTheta(j, Conjugate(z), tau), Conjugate(JacobiTheta(j, z, Neg(Conjugate(tau)))))),
    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