A013678 Decimal expansion of zeta(20).

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• cons
• nonn

Examples

			1.00000095396203387279611315203868344934594379418741059575005648985113...
		

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].

Programs

Mathematica

RealDigits[Zeta[20],10,120][[1]] (* Harvey P. Dale, Jun 21 2015 *)

Formula

zeta(20) = Sum_{n >= 1} (A010052(n)/n^10) = Sum_{n >= 1} ( (floor(sqrt(n))-floor(sqrt(n-1)))/n^10 ). - Mikael Aaltonen, Mar 06 2015

zeta(20) = 174611 * Pi^20 / 1531329465290625. - Vaclav Kotesovec, May 15 2019

zeta(20) = Product_{k>=1} 1/(1 - 1/prime(k)^20). - Vaclav Kotesovec, May 02 2020