Fungrim entry: 921f34

\lambda(\tau) = 16 q - 128 {q}^{2} + 704 {q}^{3} - 3072 {q}^{4} + 11488 {q}^{5} - 38400 {q}^{6} + \ldots \; \text{ where } q = {e}^{\pi i \tau}

Assumptions:

\tau \in \mathbb{H}

References:

https://oeis.org/A115977

TeX:

\lambda(\tau) = 16 q - 128 {q}^{2} + 704 {q}^{3} - 3072 {q}^{4} + 11488 {q}^{5} - 38400 {q}^{6} + \ldots \; \text{ where } q = {e}^{\pi i \tau}

\tau \in \mathbb{H}

Definitions:

Fungrim symbol	Notation	Short description
`ModularLambda`	$\lambda(\tau)$	Modular lambda function
`Pow`	${a}^{b}$	Power
`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("921f34"),
    Formula(EqualQSeriesEllipsis(ModularLambda(tau), tau, q, Sub(Add(Sub(Add(Sub(Mul(16, q), Mul(128, Pow(q, 2))), Mul(704, Pow(q, 3))), Mul(3072, Pow(q, 4))), Mul(11488, Pow(q, 5))), Mul(38400, Pow(q, 6))), Equal(q, Exp(Mul(Mul(Pi, ConstI), tau))))),
    Variables(tau),
    Assumptions(Element(tau, HH)),
    References("https://oeis.org/A115977"))

Topics using this entry

Modular lambda function