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Fungrim entry: ac236f

a(n)(1)n+1e2πn32n3/4,  n   where a(n)=[qn]λ(τ)  (q=eπiτ)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)
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)
Fungrim symbol Notation Short description
Powab{a}^{b} Power
Expez{e}^{z} Exponential function
Piπ\pi The constant pi (3.14...)
Sqrtz\sqrt{z} Principal square root
Infinity\infty Positive infinity
ModularLambdaλ(τ)\lambda(\tau) Modular lambda function
ConstIii Imaginary unit
Source code for this entry:
    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))))))),

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2021-03-15 19:12:00.328586 UTC