# 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))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-04-08 16:14:44.404316 UTC