A134470 Continued fraction expansion of -zeta(1/2)/sqrt(2*Pi).

0, 1, 1, 2, 1, 1, 8, 1, 5, 1, 1, 1, 12, 5, 1, 1, 5, 1, 12, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 2, 2, 2, 1, 11, 1, 6, 1, 3, 2, 1, 1, 1, 1, 1, 2, 6, 7, 1, 4, 2, 1, 1, 1, 13, 1, 1, 1, 2, 4, 2, 11, 1, 2, 5, 1, 8, 1, 78, 10, 1, 64, 1, 29, 1, 3, 1, 1, 1, 2, 1, 12, 1, 2, 1, 4, 1, 2, 1, 2, 32, 1, 92, 1, 14, 1, 10, 12, 2, 3, 16, 2, 1, 1, 1, 1, 8, 3, 15, 1, 2, 2, 1, 4, 4, 2, 8, 1, 1557, 3, 1, 69, 1, 5, 3, 11, 1, 1

Offset: 0

Author

Hans J. H. Tuenter, Oct 27 2007

Keywords

• cofr
• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Hans J. H. Tuenter, Overshoot in the Case of Normal Variables: Chernoff's Integral, Latta's Observation and Wijsman's Sum, Sequential Analysis, 26(4) (2007) 481-488.

Crossrefs

Cf. A134469 (Decimal expansion), A134471 (Numerators of continued fraction convergents), A134472 (Denominators of continued fraction convergents).

Programs

Maple

Digits:=100; cfrac(-Zeta(1/2)/sqrt(2*Pi),30,'quotients');

Mathematica

ContinuedFraction[ -Zeta[1/2]/Sqrt[2 \[Pi]], 100] (* J. Mulder (jasper.mulder(AT)planet.nl), Jan 25 2010 *)

PARI

default(realprecision,1000);
c=-zeta(1/2)/sqrt(2*Pi); /* == 0.582597157... (A134469) */
contfrac(c) /* gives 967 terms */

Extensions

More terms from J. Mulder (jasper.mulder(AT)planet.nl), Jan 25 2010