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 A013666 Decimal expansion of zeta(8). 45
 1, 0, 0, 4, 0, 7, 7, 3, 5, 6, 1, 9, 7, 9, 4, 4, 3, 3, 9, 3, 7, 8, 6, 8, 5, 2, 3, 8, 5, 0, 8, 6, 5, 2, 4, 6, 5, 2, 5, 8, 9, 6, 0, 7, 9, 0, 6, 4, 9, 8, 5, 0, 0, 2, 0, 3, 2, 9, 1, 1, 0, 2, 0, 2, 6, 5, 2, 5, 8, 2, 9, 5, 2, 5, 7, 4, 7, 4, 8, 8, 1, 4, 3, 9, 5, 2, 8, 7, 2, 3, 0, 3, 7, 2, 3, 7, 1, 9, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS This sequence is also the decimal expansion of Pi^8/9450. - Mohammad K. Azarian, Mar 03 2008 REFERENCES M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 811. LINKS Table of n, a(n) for n=1..99. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. FORMULA zeta(8) = 2/3*2^8/(2^8 - 1)*( Sum_{n even} n^2*p(n)/(n^2 - 1)^9 ), where p(n) = 5*n^8 + 60*n^6 + 126*n^4 + 60*n^2 + 5 is a row polynomial of A091043. See A013662, A013664, A013668 and A013670. - Peter Bala, Dec 05 2013 zeta(8) = Sum_{n >= 1} (A010052(n)/n^4). - Mikael Aaltonen, Feb 20 2015 zeta(8) = Product_{k>=1} 1/(1 - 1/prime(k)^8). - Vaclav Kotesovec, May 02 2020 From Wolfdieter Lang, Sep 16 2020 (Start): zeta(8) = (1/7!)*Integral_{0..infinity} x^7/(exp(x) - 1) dx. See Abramowitz-Stegun, 23.2.7., for s=8, p. 807. The value of the integral is 8*Pi^8/15 = 5060.54987... . zeta(8) = (2^7/(127*7!))*Integral_{0..infinity} x^7/(exp(x) + 1) dx. See Abramowitz-Stegun, 23.2.8., for s=8, p. 807. The prefactor is 8/40005. The value of the integral is (127/240)*Pi^8 = 5021.014329... .(End) Equals A092736/9450. - R. J. Mathar, Jan 07 2021 EXAMPLE 1.00407735619794433937868523850865246525896079064985002032911020265... MAPLE Digits := 100 : evalf(Pi^8/9450) ; # R. J. Mathar, Jan 07 2021 MATHEMATICA RealDigits[Zeta[8], 10, 100][[1]] (* Vincenzo Librandi, Feb 15 2015 *) CROSSREFS Cf. A013662, A013664, A013668, A013670. Sequence in context: A070433 A169821 A170990 * A196533 A200518 A016682 Adjacent sequences: A013663 A013664 A013665 * A013667 A013668 A013669 KEYWORD nonn,cons AUTHOR N. J. A. Sloane STATUS approved

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Last modified July 13 01:42 EDT 2024. Contains 374259 sequences. (Running on oeis4.)