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Fungrim entry: 921f34

λ ⁣(τ)=16q128q2+704q33072q4+11488q538400q6+   where q=eπiτ\lambda\!\left(\tau\right) = 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:τH\tau \in \mathbb{H}
References:
  • https://oeis.org/A115977
TeX:
\lambda\!\left(\tau\right) = 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
ModularLambdaλ ⁣(τ)\lambda\!\left(\tau\right) Modular lambda function
Powab{a}^{b} Power
Expez{e}^{z} Exponential function
ConstPiπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
HHH\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(ConstPi, ConstI), tau))))),
    Variables(tau),
    Assumptions(Element(tau, HH)),
    References("https://oeis.org/A115977"))

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2019-09-16 21:17:18.797188 UTC