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A371530
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Decimal expansion of Product_{k>=1} (1 - (-1)^k/Lucas(k)).
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5
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1, 5, 0, 2, 1, 8, 0, 0, 4, 4, 3, 3, 2, 4, 5, 6, 7, 6, 9, 1, 2, 0, 7, 6, 2, 5, 8, 1, 7, 6, 5, 5, 6, 9, 9, 8, 8, 0, 2, 7, 1, 5, 2, 5, 8, 0, 8, 8, 8, 8, 8, 3, 6, 4, 4, 5, 1, 5, 0, 1, 5, 5, 1, 1, 7, 0, 7, 8, 7, 4, 1, 9, 3, 3, 3, 7, 5, 9, 4, 6, 3, 2, 9, 9, 3, 4, 4, 3, 7, 1, 9, 2, 1, 5, 9, 4, 8, 3, 9, 2, 4, 1, 0, 8, 8
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OFFSET
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1,2
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LINKS
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FORMULA
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Equals Product_{k>=2} (1 - (-1)^k/A000032(k)).
Equals 2 * phi^(1/4) * eta(2*tau_0)^2 * eta(6*tau_0) / (eta(3*tau_0) * eta(4*tau_0)), where phi is the golden ratio (A001622), tau_0 = i*log(phi)/Pi, and i = sqrt(-1) (Duverney et al., 2022).
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EXAMPLE
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1.50218004433245676912076258176556998802715258088888...
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MATHEMATICA
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With[{eta = DedekindEta, tau0 = Log[GoldenRatio]*I/Pi}, RealDigits[2 * Surd[GoldenRatio, 4] * eta[2*tau0]^2 * eta[6*tau0]/(eta[3*tau0] * eta[4*tau0]), 10, 120][[1]]]
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PROG
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(PARI) prodinf(k = 1, 1 - (-1)^k/(fibonacci(k-1) + fibonacci(k+1)))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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