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 A334411 Decimal expansion of Product_{k>=1} (1 + 1/k^8). 2
 2, 0, 0, 8, 1, 5, 6, 0, 5, 4, 9, 9, 2, 7, 4, 5, 3, 1, 5, 1, 4, 9, 0, 3, 9, 4, 8, 2, 3, 2, 3, 4, 1, 3, 6, 9, 2, 1, 1, 9, 5, 3, 2, 1, 5, 9, 8, 3, 0, 9, 5, 0, 9, 7, 8, 7, 7, 0, 7, 4, 2, 9, 9, 6, 1, 7, 4, 2, 2, 7, 2, 5, 1, 1, 3, 8, 0, 5, 5, 2, 0, 9, 3, 4, 0, 6, 0, 5, 0, 1, 0, 2, 0, 2, 6, 9, 6, 3, 0, 3, 2, 1, 8, 7, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..105. FORMULA Equals exp(Sum_{j>=1} (-(-1)^j*Zeta(8*j)/j)). Equals (cos(sqrt(4 - 2*sqrt(2))*Pi) + cos(sqrt(4 + 2*sqrt(2))*Pi) + cosh(sqrt(4 - 2*sqrt(2))*Pi) + cosh(sqrt(4 + 2*sqrt(2))*Pi) - 2*cos(sqrt(2 - sqrt(2))*Pi) * cosh(sqrt(2 - sqrt(2))*Pi) - 2*cos(sqrt(2 + sqrt(2))*Pi) * cosh(sqrt(2 + sqrt(2))*Pi)) / (8*Pi^4). EXAMPLE 2.00815605499274531514903948232341369211953215983095097877074299617422... MAPLE evalf(Product(1 + 1/j^8, j = 1..infinity), 120); MATHEMATICA RealDigits[Chop[N[Product[(1 + 1/n^8), {n, 1, Infinity}], 120]]][[1]] PROG (PARI) default(realprecision, 120); exp(sumalt(j=1, -(-1)^j*zeta(8*j)/j)) CROSSREFS Cf. A156648, A073017, A258870, A307216, A258871. Cf. A109219, A175615, A175616, A175617, A175619. Sequence in context: A192058 A021502 A319568 * A028698 A013667 A091933 Adjacent sequences: A334408 A334409 A334410 * A334412 A334413 A334414 KEYWORD nonn,cons AUTHOR Vaclav Kotesovec, Apr 27 2020 STATUS approved

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Last modified April 14 05:31 EDT 2024. Contains 371655 sequences. (Running on oeis4.)