A084233 Decimal expansion of area under the curve Zeta(1/2 + t*I) from zero to its first nontrivial zero (A058303).

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

Offset: 2

Author

Robert G. Wilson v, May 11 2003

Keywords

• nonn
• cons

Examples

			13.832853042...
		

Links

• Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros
• Index entries for zeta function.

Crossrefs

Cf. A058303.

Programs

Mathematica

digits = 100; NIntegrate[ Zeta[1/2 + t*I] // Abs, {t, 0, ZetaZero[1] // Im}, WorkingPrecision -> digits+5] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Mar 05 2013 *)

PARI

intnum(t=0,solve(s=14,15,imag(zeta(1/2+I*s))),abs(zeta(1/2+I*t))) /* Brad Chalfan (brad(AT)chalfan.net), Aug 31 2010 */

Extensions

More terms from Brad Chalfan (brad(AT)chalfan.net), Aug 31 2010