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Fungrim entry: b3fc6d

θ3 ⁣(z,τ)=θ4 ⁣(z+12,τ)\theta_{3}\!\left(z , \tau\right) = \theta_{4}\!\left(z + \frac{1}{2} , \tau\right)
Assumptions:z∈C  and⁡  τ∈Hz \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}
TeX:
\theta_{3}\!\left(z , \tau\right) = \theta_{4}\!\left(z + \frac{1}{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("b3fc6d"),
    Formula(Equal(JacobiTheta(3, z, tau), JacobiTheta(4, Add(z, Div(1, 2)), tau))),
    Variables(z, tau),
    Assumptions(And(Element(z, CC), Element(tau, HH))))

Topics using this entry

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