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Fungrim entry: 936694

(30D1315D0D1D2+D02D3)2+32(D0D23D12)3+π2(D0D23D12)2D010=0   where Dr=drdτrθj ⁣(0,τ){\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{1,2,3,4}andτHj \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
Powab{a}^{b} Power
ConstPiπ\pi The constant pi (3.14...)
Derivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Derivative
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
HHH\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(Subscript(D, 1), 3)), Mul(Mul(Mul(15, Subscript(D, 0)), Subscript(D, 1)), Subscript(D, 2))), Mul(Pow(Subscript(D, 0), 2), Subscript(D, 3))), 2), Mul(32, Pow(Sub(Mul(Subscript(D, 0), Subscript(D, 2)), Mul(3, Pow(Subscript(D, 1), 2))), 3))), Mul(Mul(Pow(ConstPi, 2), Pow(Sub(Mul(Subscript(D, 0), Subscript(D, 2)), Mul(3, Pow(Subscript(D, 1), 2))), 2)), Pow(Subscript(D, 0), 10))), 0), Equal(Subscript(D, r), Derivative(JacobiTheta(j, 0, tau), 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.

2019-09-20 18:07:53.062439 UTC