A201995 Decimal expansion of the absolute value of zeta'''(2), the third derivative of the Riemann zeta function at 2.

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

Offset: 1

Author

R. J. Mathar, Dec 07 2011

Keywords

• cons
• nonn

Examples

			zeta'''(2) = -6.00014580284304486564394121753784..
		

Links

• Jason Bard, Table of n, a(n) for n = 1..2000
• B. K. Choudhury, The Riemann zeta-function and its derivatives, Proc. R. Soc. Lond A 445 (1995) 477-499.
• Michael I. Shamos, A catalog of the real numbers, (2007). See p. 21.

Crossrefs

Cf. A013661, A073002, A201994.

Programs

Maple

evalf(Zeta(3,2));

Mathematica

RealDigits[ Zeta'''[2], 10, 93] // First (* Jean-François Alcover, Feb 20 2013 *)

Formula

zeta'''(2)= -Sum_{k>=1} log^3(k)/k^2.

Equals 3! + Sum_{k>=0} (-1)^k*gamma(3+k)/k!, where gamma(.) are the Stieltjes constants A001620, A082633, A086279 etc. [Choudhury, Thm. 4]