Fungrim entry: cc579c

$E_{4}\!\left(\tau\right) = \frac{1}{2} \left({a}^{8} + {b}^{8} + {c}^{8}\right)\; \text{ where } a = \theta_{2}\!\left(0 , \tau\right),\,b = \theta_{3}\!\left(0 , \tau\right),\,c = \theta_{4}\!\left(0 , \tau\right)$
Assumptions:$\tau \in \mathbb{H}$
TeX:
E_{4}\!\left(\tau\right) = \frac{1}{2} \left({a}^{8} + {b}^{8} + {c}^{8}\right)\; \text{ where } a = \theta_{2}\!\left(0 , \tau\right),\,b = \theta_{3}\!\left(0 , \tau\right),\,c = \theta_{4}\!\left(0 , \tau\right)

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
EisensteinE$E_{k}\!\left(\tau\right)$ Normalized Eisenstein series
Pow${a}^{b}$ Power
JacobiTheta$\theta_{j}\!\left(z , \tau\right)$ Jacobi theta function
HH$\mathbb{H}$ Upper complex half-plane
Source code for this entry:
Entry(ID("cc579c"),
Formula(Equal(EisensteinE(4, tau), Where(Mul(Div(1, 2), Add(Add(Pow(a, 8), Pow(b, 8)), Pow(c, 8))), Equal(a, JacobiTheta(2, 0, tau)), Equal(b, JacobiTheta(3, 0, tau)), Equal(c, JacobiTheta(4, 0, tau))))),
Variables(tau),
Assumptions(Element(tau, HH)))

Topics using this entry

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

2019-08-19 14:38:23.809000 UTC