Assumptions:
TeX:
\theta_{3}\!\left(4 z , 4 \tau\right) = \frac{\theta_{3}\!\left(\frac{1}{8} - z , \tau\right) \theta_{3}\!\left(\frac{1}{8} + z , \tau\right) \theta_{3}\!\left(\frac{3}{8} - z , \tau\right) \theta_{3}\!\left(\frac{3}{8} + z , \tau\right)}{\theta_{3}\!\left(0 , \tau\right) \theta_{4}\!\left(0 , \tau\right) \theta_{3}\!\left(\frac{1}{4} , \tau\right)} z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}
Definitions:
Fungrim symbol | Notation | Short description |
---|---|---|
JacobiTheta | Jacobi theta function | |
CC | Complex numbers | |
HH | Upper complex half-plane |
Source code for this entry:
Entry(ID("0096a8"), Formula(Equal(JacobiTheta(3, Mul(4, z), Mul(4, tau)), Div(Mul(Mul(Mul(JacobiTheta(3, Sub(Div(1, 8), z), tau), JacobiTheta(3, Add(Div(1, 8), z), tau)), JacobiTheta(3, Sub(Div(3, 8), z), tau)), JacobiTheta(3, Add(Div(3, 8), z), tau)), Mul(Mul(JacobiTheta(3, 0, tau), JacobiTheta(4, 0, tau)), JacobiTheta(3, Div(1, 4), tau))))), Variables(z, tau), Assumptions(And(Element(z, CC), Element(tau, HH))))