A334448 Decimal expansion of Product_{k>=1} (1 - 1/A002145(k)^4).

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

Table of n, a(n) for n=0..105.

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

Cf. A002145, A243379, A334427, A334452.

Sequence in context: A002388 A248080 A278828 * A011116 A106334 A089739

Adjacent sequences: A334445 A334446 A334447 * A334449 A334450 A334451

Keyword

nonn,cons

Author

Vaclav Kotesovec, Apr 30 2020

Extensions

More digits from Vaclav Kotesovec, Jun 27 2020

Status

approved