Fungrim entry: e96684

\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:

\tau \in \mathbb{H}

TeX:

\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}

Definitions:

Fungrim symbol	Notation	Short description
`ModularLambda`	$\lambda(\tau)$	Modular lambda function
`Product`	$\prod_{n} f(n)$	Product
`Pow`	${a}^{b}$	Power
`Infinity`	$\infty$	Positive infinity
`Exp`	${e}^{z}$	Exponential function
`Pi`	$\pi$	The constant pi (3.14...)
`ConstI`	$i$	Imaginary unit
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("e96684"),
    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)))))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

Topics using this entry

Modular lambda function