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Fungrim entry: 28b4c3

θ3 ⁣(z,τ+n)={θ3 ⁣(z,τ),n evenθ4 ⁣(z,τ),n odd\theta_{3}\!\left(z , \tau + n\right) = \begin{cases} \theta_{3}\!\left(z , \tau\right), & n \text{ even}\\\theta_{4}\!\left(z , \tau\right), & n \text{ odd}\\ \end{cases}
Assumptions:zC  and  τH  and  nZz \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
\theta_{3}\!\left(z , \tau + n\right) = \begin{cases} \theta_{3}\!\left(z , \tau\right), & n \text{ even}\\\theta_{4}\!\left(z , \tau\right), & n \text{ odd}\\ \end{cases}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
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
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Equal(JacobiTheta(3, z, Add(tau, n)), Cases(Tuple(JacobiTheta(3, z, tau), Even(n)), Tuple(JacobiTheta(4, z, tau), Odd(n))))),
    Variables(z, tau, n),
    Assumptions(And(Element(z, CC), Element(tau, HH), Element(n, ZZ))))

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