A094643 Continued fraction for log(Pi/2).

0, 2, 4, 1, 1, 1, 33, 1, 4, 2, 1, 2, 1, 17, 1, 1, 4, 4, 1, 2, 1, 3, 1, 3, 1, 17, 54, 1, 4, 1, 3, 38, 1, 2, 1, 1, 2, 3, 4, 3, 1, 4, 1, 8, 4, 2, 1, 4, 12, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 16, 3, 2, 4, 1, 5, 1, 12, 1, 2, 14, 1, 1, 1, 2, 3, 2, 16, 3, 4, 4, 1, 1, 10, 198, 2, 6, 2, 1, 2, 3, 1, 2

Offset: 0

Author

Jonathan Sondow and Robert G. Wilson v, May 18 2004

Keywords

• cofr
• easy
• nonn

References

• G. Boros and V. Moll, Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals, Cambridge University Press, Cambridge, 2004, Chap. 7.
• J. Borwein and P. Borwein, Pi and the AGM, John Wiley & Sons, New York, 1987, Chap. 11.

Links

• D. Huylebrouck, Similarities in irrationality proofs for Pi, ln2, zeta(2) and zeta(3), Amer. Math. Monthly 108 (2001) 222-231.
• Jonathan Sondow, A faster product for pi and a new integral for ln(pi/2), arXiv:math/0401406 [math.NT], 2004; Amer. Math. Monthly 112 (2005), 729-734 and 113 (2006), 670.

Crossrefs

Cf. A094642 (decimal expansion).

Programs

Mathematica

ContinuedFraction[ Log[Pi/2], 100]

Extensions

Offset changed by Andrew Howroyd, Aug 07 2024