- G = 0.915 965 594 177 219 015 054 603 514 932 384 110 774 …
Catalan's constant was named after Eugène Charles Catalan.
Integral identities 
Some identities include
where K(t) is a complete elliptic integral of the first kind.
Simon Plouffe gives an infinite collection of identities between the trigamma function, π2 and Catalan's constant; these are expressible as paths on a graph.
It also appears in connection with the hyperbolic secant distribution.
Quickly converging series 
The following two formulas involve quickly converging series, and are thus appropriate for numerical computation:
The theoretical foundations for such series is given by Broadhurst (the first formula) and Ramanujan (the second formula). The algorithms for fast evaluation of the Catalan constant is constructed by E. Karatsuba.
Known digits 
The number of known digits of Catalan's constant G has increased dramatically during the last decades. This is due both to the increase of performance of computers as well as to algorithmic improvements.
|Date||Decimal digits||Computation performed by|
|1858||19||Carl Johan Danielsson Hill|
|1864||14||Eugène Charles Catalan|
|1877||20||James W. L. Glaisher|
|1913||32||James W. L. Glaisher|
|1990||20,000||Greg J. Fee|
|1996||50,000||Greg J. Fee|
|August 14, 1996||100,000||Greg J. Fee & Simon Plouffe|
|September 29, 1996||300,000||Thomas Papanikolaou|
|January 4, 1998||12,500,000||Xavier Gourdon|
|2001||100,000,500||Xavier Gourdon & Pascal Sebah|
|2002||201,000,000||Xavier Gourdon & Pascal Sebah|
|October 2006||5,000,000,000||Shigeru Kondo & Steve Pagliarulo|
|August 2008||10,000,000,000||Shigeru Kondo & Steve Pagliarulo|
|January 31, 2009||15,510,000,000||Alexander J. Yee & Raymond Chan|
|April 16, 2009||31,026,000,000||Alexander J. Yee & Raymond Chan|
|April 6, 2013||100,000,000,000||Robert J. Setti|
See also 
- Broadhurst, D.J. (1998). "Polylogarithmic ladders, hypergeometric series and the ten millionth digits of ζ(3) and ζ(5)". arXiv:math.CA/9803067.
- B.C. Berndt, Ramanujan's Notebook, Part I., Springer Verlag (1985)
- E.A. Karatsuba, Fast evaluation of transcendental functions, Probl. Inf. Transm. Vol.27, No.4, pp. 339–360 (1991)
- E.A. Karatsuba, Fast computation of some special integrals of mathematical physics. Scientific Computing, Validated Numerics, Interval Methods, W.Krämer, J.W.von Gudenberg, eds.; pp. 29–41, (2001)
- Gourdon, X., Sebah, P; Constants and Records of Computation
- Shigeru Kondo's website
- Constants and Records of Computation
- Large Computations
- 100 Billion Digits Catalan's Constant Complete
- Victor Adamchik, 33 representations for Catalan's constant (undated)
- Adamchik,, Victor (2002). "A certain series associated with Catalan's constant". Zeitschr. f. Analysis und ihre Anwendungen (ZAA) 21 (3): 1–10. MR 1929434.
- Plouffe, Simon (1993). "A few identities (III) with Catalan". (Provides over one hundred different identities).
- Simon Plouffe, A few identities with Catalan constant and Pi^2, (1999) (Provides a graphical interpretation of the relations)
- Weisstein, Eric W., "Catalan's Constant", MathWorld.
- Catalan constant: Generalized power series at the Wolfram Functions Site
- Greg Fee, Catalan's Constant (Ramanujan's Formula) (1996) (Provides the first 300,000 digits of Catalan's constant.).
- Fee, Greg (1990), Computation of Catalan's constant using Ramanujan's Formula, Proceedings of the ISSAC '90, pp. 157–160, doi:10.1145/96877.96917
- Bradley, David M. (1999). "A class of series acceleration formulae for Catalan's constant". The Ramanujan Journal 3 (2): 159–173. doi:10.1023/A:1006945407723. MR 1703281.
- Bradley, David M. (2007). "A class of series acceleration formulae for Catalan's constant". arXiv:0706.0356.
- Bradley, David M. (2001), Representations of Catalan's constant