Fungrim entry: 936694

{\left(30 D_{1}^{3} - 15 D_{0} D_{1} D_{2} + D_{0}^{2} D_{3}\right)}^{2} + 32 {\left(D_{0} D_{2} - 3 D_{1}^{2}\right)}^{3} + {\pi}^{2} {\left(D_{0} D_{2} - 3 D_{1}^{2}\right)}^{2} D_{0}^{10} = 0\; \text{ where } D_{r} = \frac{d^{r}}{{d \tau}^{r}} \theta_{j}\!\left(0 , \tau\right)

Assumptions:

j \in \left\{1, 2, 3, 4\right\} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}

TeX:

{\left(30 D_{1}^{3} - 15 D_{0} D_{1} D_{2} + D_{0}^{2} D_{3}\right)}^{2} + 32 {\left(D_{0} D_{2} - 3 D_{1}^{2}\right)}^{3} + {\pi}^{2} {\left(D_{0} D_{2} - 3 D_{1}^{2}\right)}^{2} D_{0}^{10} = 0\; \text{ where } D_{r} = \frac{d^{r}}{{d \tau}^{r}} \theta_{j}\!\left(0 , \tau\right)

j \in \left\{1, 2, 3, 4\right\} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}

Definitions:

Fungrim symbol	Notation	Short description
`Pow`	${a}^{b}$	Power
`Pi`	$\pi$	The constant pi (3.14...)
`ComplexDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative
`JacobiTheta`	$\theta_{j}\!\left(z , \tau\right)$	Jacobi theta function
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("936694"),
    Formula(Where(Equal(Add(Add(Pow(Add(Sub(Mul(30, Pow(D_(1), 3)), Mul(Mul(Mul(15, D_(0)), D_(1)), D_(2))), Mul(Pow(D_(0), 2), D_(3))), 2), Mul(32, Pow(Sub(Mul(D_(0), D_(2)), Mul(3, Pow(D_(1), 2))), 3))), Mul(Mul(Pow(Pi, 2), Pow(Sub(Mul(D_(0), D_(2)), Mul(3, Pow(D_(1), 2))), 2)), Pow(D_(0), 10))), 0), Def(D_(r), ComplexDerivative(JacobiTheta(j, 0, tau), For(tau, tau, r))))),
    Variables(j, tau),
    Assumptions(And(Element(j, Set(1, 2, 3, 4)), Element(tau, HH))))

Fungrim entry: 936694

Topics using this entry