A096418 Decimal expansion of Sum_{k >= 1} sin(k)/k^2.

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

Offset: 1

Author

N. J. A. Sloane, Aug 16 2004

Keywords

• nonn
• cons

Comments

Also, decimal expansion of the imaginary part of Sum_{k>=1} e^(i*k)/k^2. [Bruno Berselli, Mar 24 2013]

Examples

			1.013959132360768504294574338885914687561179280077717316877048512268137...
		

Links

• I. Rosenholtz, Tangent sequences, world records, ..., Math. Mag., 72 (No. 5, 1999), 367-376.

Crossrefs

Cf. A096444, A096464.

Cf. A122143 (decimal expansion of Sum_{k >= 1} cos(k)/k^2).

Programs

Mathematica

$MaxExtraPrecision = 128; RealDigits[ Chop[ N[ I/2*(PolyLog[2, E^-I] - PolyLog[2, E^I]), 105]]][[1]] (* Robert G. Wilson v, Aug 16 2004 *)

PARI

imag(polylog(2,exp(I))) \\ Charles R Greathouse IV, Jul 14 2014

Extensions

More terms from Robert G. Wilson v, Aug 17 2004

Sequence checked by T. D. Noe, Aug 21 2006