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Fungrim entry: 6b2078

θ1 ⁣(z,τ+1)=eπi/4θ1 ⁣(z,τ)\theta_{1}\!\left(z , \tau + 1\right) = {e}^{\pi i / 4} \theta_{1}\!\left(z , \tau\right)
Assumptions:zCandτHz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}
TeX:
\theta_{1}\!\left(z , \tau + 1\right) = {e}^{\pi i / 4} \theta_{1}\!\left(z , \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
Expez{e}^{z} Exponential function
ConstPiπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("6b2078"),
    Formula(Equal(JacobiTheta(1, z, Add(tau, 1)), Mul(Exp(Div(Mul(ConstPi, ConstI), 4)), JacobiTheta(1, z, 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.

2019-09-19 20:12:49.583742 UTC