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Fungrim entry: 4448f1

θ4 ⁣(z+2n,τ)=θ3 ⁣(z,τ)\theta_4\!\left(z + 2 n, \tau\right) = \theta_3\!\left(z, \tau\right)
Assumptions:z∈C and⁡ τ∈H and⁡ n∈Zz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
TeX:
\theta_4\!\left(z + 2 n, \tau\right) = \theta_3\!\left(z, \tau\right)

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
JacobiTheta4θ4 ⁣(z,τ)\theta_4\!\left(z, \tau\right) Jacobi theta function
JacobiTheta3θ3 ⁣(z,τ)\theta_3\!\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:
Entry(ID("4448f1"),
    Formula(Equal(JacobiTheta4(Add(z, Mul(2, n)), tau), JacobiTheta3(z, tau))),
    Variables(z, tau, n),
    Assumptions(And(Element(z, CC), Element(tau, HH), Element(n, ZZ))))

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

2019-06-18 07:49:59.356594 UTC