A013671 Decimal expansion of zeta(13).

1, 0, 0, 0, 1, 2, 2, 7, 1, 3, 3, 4, 7, 5, 7, 8, 4, 8, 9, 1, 4, 6, 7, 5, 1, 8, 3, 6, 5, 2, 6, 3, 5, 7, 3, 9, 5, 7, 1, 4, 2, 7, 5, 1, 0, 5, 8, 9, 5, 5, 0, 9, 8, 4, 5, 1, 3, 6, 7, 0, 2, 6, 7, 1, 6, 2, 0, 8, 9, 6, 7, 2, 6, 8, 2, 9, 8, 4, 4, 2, 0, 9, 8, 1, 2, 8, 9, 2, 7, 1, 3, 9, 5, 3, 2, 6, 8, 1, 3

Offset: 1

Author

N. J. A. Sloane

Keywords

• cons
• nonn

Examples

			1.0001227133475784891467518365263573957142751058955098451367026716208967...
		

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

• 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].

Crossrefs

Cf. A013663, A013667, A013669, A013671, A013675, A013677.

Programs

Mathematica

RealDigits[Zeta[13],10,120][[1]] (* Harvey P. Dale, Dec 24 2016 *)

PARI

zeta(13) \\ Charles R Greathouse IV, Apr 25 2016

Formula

From Peter Bala, Dec 04 2013: (Start)

Definition: zeta(13) = sum {n >= 1} 1/n^13.

zeta(13) = 2^13/(2^13 - 1)*( sum {n even} n^9*p(n)*p(1/n)/(n^2 - 1)^14 ), where p(n) = n^6 + 21*n^4 + 35*n^2 + 7. (End)

zeta(13) = Sum_{n >= 1} (A010052(n)/n^(13/2)) = Sum_{n >= 1} ( (floor(sqrt(n))-floor(sqrt(n-1)))/n^(13/2) ). - Mikael Aaltonen, Feb 22 2015

zeta(13) = Product_{k>=1} 1/(1 - 1/prime(k)^13). - Vaclav Kotesovec, May 02 2020