Fungrim entry: ac236f

a(n) \sim {\left(-1\right)}^{n + 1} \frac{{e}^{2 \pi \sqrt{n}}}{32 {n}^{3 / 4}}, \; n \to \infty\; \text{ where } a(n) = [q^{n}] \lambda(\tau) \; \left(q = {e}^{\pi i \tau}\right)

References:

https://oeis.org/A115977

TeX:

a(n) \sim {\left(-1\right)}^{n + 1} \frac{{e}^{2 \pi \sqrt{n}}}{32 {n}^{3 / 4}}, \; n \to \infty\; \text{ where } a(n) = [q^{n}] \lambda(\tau) \; \left(q = {e}^{\pi i \tau}\right)

Definitions:

Fungrim symbol	Notation	Short description
`Pow`	${a}^{b}$	Power
`Exp`	${e}^{z}$	Exponential function
`Pi`	$\pi$	The constant pi (3.14...)
`Sqrt`	$\sqrt{z}$	Principal square root
`Infinity`	$\infty$	Positive infinity
`ModularLambda`	$\lambda(\tau)$	Modular lambda function
`ConstI`	$i$	Imaginary unit

Source code for this entry:

Entry(ID("ac236f"),
    Formula(Where(AsymptoticTo(a(n), Mul(Pow(-1, Add(n, 1)), Div(Exp(Mul(Mul(2, Pi), Sqrt(n))), Mul(32, Pow(n, Div(3, 4))))), n, Infinity), Equal(a(n), QSeriesCoefficient(ModularLambda(tau), tau, q, n, Equal(q, Exp(Mul(Mul(Pi, ConstI), tau))))))),
    References("https://oeis.org/A115977"))

Topics using this entry

Modular lambda function