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Fungrim entry: 47f4ba

θ2 ⁣(0,yi)=1yθ3 ⁣(0,1+iy)\theta_{2}\!\left(0 , y i\right) = \frac{1}{\sqrt{y}} \theta_{3}\!\left(0 , 1 + \frac{i}{y}\right)
Assumptions:y∈(0,∞)y \in \left(0, \infty\right)
TeX:
\theta_{2}\!\left(0 , y i\right) = \frac{1}{\sqrt{y}} \theta_{3}\!\left(0 , 1 + \frac{i}{y}\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
Sqrtz\sqrt{z} Principal square root
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity∞\infty Positive infinity
Source code for this entry:
Entry(ID("47f4ba"),
    Formula(Equal(JacobiTheta(2, 0, Mul(y, ConstI)), Mul(Div(1, Sqrt(y)), JacobiTheta(3, 0, Add(1, Div(ConstI, y)))))),
    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