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A334448
Decimal expansion of Product_{k>=1} (1 - 1/A002145(k)^4).
8
9, 8, 7, 1, 6, 2, 6, 2, 5, 4, 2, 2, 2, 2, 6, 8, 5, 6, 4, 8, 2, 7, 0, 1, 2, 6, 4, 5, 7, 7, 3, 7, 0, 8, 2, 7, 7, 2, 4, 0, 3, 2, 7, 9, 7, 2, 9, 2, 8, 2, 4, 1, 4, 7, 4, 3, 4, 8, 3, 2, 6, 5, 0, 8, 5, 5, 7, 3, 0, 8, 9, 4, 7, 5, 6, 6, 7, 0, 0, 1, 8, 8, 9, 0, 8, 4, 1, 5, 0, 4, 9, 9, 8, 9, 0, 7, 3, 3, 4, 7, 7, 0, 3, 5, 3, 6
OFFSET
0,1
COMMENTS
In general, for s>1, Product_{k>=1} (1 + 1/A002145(k)^s)/(1 - 1/A002145(k)^s) = 2^s * (2^s - 1) * zeta(s) / (zeta(s, 1/4) - zeta(s, 3/4)).
REFERENCES
B. C. Berndt, Ramanujan's notebook part IV, Springer-Verlag, 1994, p. 64-65.
LINKS
Ph. Flajolet and I. Vardi, Zeta function expansions of some classical constants, Feb 18 1996, p. 7-8.
R. J. Mathar, Table of Dirichlet L-series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], 2010-2015, p. 26 (case 4 3 4 = 1/A334448).
FORMULA
A334447 / A334448 = 1/(PolyGamma(3, 1/4)/(8*Pi^4) - 1).
A334446 * A334448 = 96/Pi^4.
EXAMPLE
0.98716262542222685648270126457737082772403279729282414743483...
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Apr 30 2020
EXTENSIONS
More digits from Vaclav Kotesovec, Jun 27 2020
STATUS
approved