Fungrim entry: 278274

\frac{\theta'''_{1}\!\left(0 , \tau\right)}{\theta'_{1}\!\left(0 , \tau\right)} = \frac{\theta''_{2}\!\left(0 , \tau\right)}{\theta_{2}\!\left(0 , \tau\right)} + \frac{\theta''_{3}\!\left(0 , \tau\right)}{\theta_{3}\!\left(0 , \tau\right)} + \frac{\theta''_{4}\!\left(0 , \tau\right)}{\theta_{4}\!\left(0 , \tau\right)}

Assumptions:

\tau \in \mathbb{H}

TeX:

\frac{\theta'''_{1}\!\left(0 , \tau\right)}{\theta'_{1}\!\left(0 , \tau\right)} = \frac{\theta''_{2}\!\left(0 , \tau\right)}{\theta_{2}\!\left(0 , \tau\right)} + \frac{\theta''_{3}\!\left(0 , \tau\right)}{\theta_{3}\!\left(0 , \tau\right)} + \frac{\theta''_{4}\!\left(0 , \tau\right)}{\theta_{4}\!\left(0 , \tau\right)}

\tau \in \mathbb{H}

Definitions:

Fungrim symbol	Notation	Short description
`JacobiTheta`	$\theta_{j}\!\left(z , \tau\right)$	Jacobi theta function
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("278274"),
    Formula(Equal(Div(JacobiTheta(1, 0, tau, 3), JacobiTheta(1, 0, tau, 1)), Add(Add(Div(JacobiTheta(2, 0, tau, 2), JacobiTheta(2, 0, tau)), Div(JacobiTheta(3, 0, tau, 2), JacobiTheta(3, 0, tau))), Div(JacobiTheta(4, 0, tau, 2), JacobiTheta(4, 0, tau))))),
    Variables(tau),
    Assumptions(And(Element(tau, HH))))

Topics using this entry

Differential equations for Jacobi theta functions