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Fungrim entry: ac236f

a ⁣(n)(1)n+1e2πn32n3/4,  n   where a ⁣(n)=[qn]λ ⁣(τ)  (q=eπiτ)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
Powab{a}^{b} Power
Expez{e}^{z} Exponential function
ConstPiπ\pi The constant pi (3.14...)
Sqrtz\sqrt{z} Principal square root
Infinity\infty Positive infinity
ModularLambdaλ ⁣(τ)\lambda\!\left(\tau\right) Modular lambda function
ConstIii 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"))

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2019-09-19 20:12:49.583742 UTC