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Fungrim entry: 81550a

θ4 ⁣(0,1+yi)=θ3 ⁣(0,yi)\theta_{4}\!\left(0 , 1 + y i\right) = \theta_{3}\!\left(0 , y i\right)
Assumptions:y∈(0,∞)y \in \left(0, \infty\right)
TeX:
\theta_{4}\!\left(0 , 1 + y i\right) = \theta_{3}\!\left(0 , y i\right)

y \in \left(0, \infty\right)
Definitions:
Fungrim symbol Notation Short description
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
ConstIii Imaginary unit
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity∞\infty Positive infinity
Source code for this entry:
Entry(ID("81550a"),
    Formula(Equal(JacobiTheta(4, 0, Add(1, Mul(y, ConstI))), JacobiTheta(3, 0, Mul(y, ConstI)))),
    Variables(y),
    Assumptions(Element(y, OpenInterval(0, Infinity))))

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