Fungrim home page

Fungrim entry: e96684

λ(τ)=16qk=1(1+q2k1+q2k1)8   where q=eπiτ\lambda(\tau) = 16 q \prod_{k=1}^{\infty} {\left(\frac{1 + {q}^{2 k}}{1 + {q}^{2 k - 1}}\right)}^{8}\; \text{ where } q = {e}^{\pi i \tau}
Assumptions:τH\tau \in \mathbb{H}
\lambda(\tau) = 16 q \prod_{k=1}^{\infty} {\left(\frac{1 + {q}^{2 k}}{1 + {q}^{2 k - 1}}\right)}^{8}\; \text{ where } q = {e}^{\pi i \tau}

\tau \in \mathbb{H}
Fungrim symbol Notation Short description
ModularLambdaλ(τ)\lambda(\tau) Modular lambda function
Productnf(n)\prod_{n} f(n) Product
Powab{a}^{b} Power
Infinity\infty Positive infinity
Expez{e}^{z} Exponential function
Piπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
    Formula(Equal(ModularLambda(tau), Where(Mul(Mul(16, q), Product(Pow(Div(Add(1, Pow(q, Mul(2, k))), Add(1, Pow(q, Sub(Mul(2, k), 1)))), 8), For(k, 1, Infinity))), Equal(q, Exp(Mul(Mul(Pi, ConstI), 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.

2021-03-15 19:12:00.328586 UTC