# Fungrim entry: ac236f

$a\!\left(n\right) \sim {\left(-1\right)}^{n + 1} \frac{{e}^{2 \pi \sqrt{n}}}{32 {n}^{3 / 4}}, \; n \to \infty\; \text{ where } a\!\left(n\right) = [q^{n}] \lambda\!\left(\tau\right) \; \left(q = {e}^{\pi i \tau}\right)$
References:
• https://oeis.org/A115977
TeX:
a\!\left(n\right) \sim {\left(-1\right)}^{n + 1} \frac{{e}^{2 \pi \sqrt{n}}}{32 {n}^{3 / 4}}, \; n \to \infty\; \text{ where } a\!\left(n\right) = [q^{n}] \lambda\!\left(\tau\right) \; \left(q = {e}^{\pi i \tau}\right)
Definitions:
Fungrim symbol Notation Short description
Pow${a}^{b}$ Power
Exp${e}^{z}$ Exponential function
ConstPi$\pi$ The constant pi (3.14...)
Sqrt$\sqrt{z}$ Principal square root
Infinity$\infty$ Positive infinity
ModularLambda$\lambda\!\left(\tau\right)$ 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, ConstPi), 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(ConstPi, ConstI), tau))))))),
References("https://oeis.org/A115977"))

## Topics using this entry

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

2019-09-19 20:12:49.583742 UTC