OFFSET
1,2
REFERENCES
Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.7.2, p. 55.
I.S. Gradshteyn and I.M. Ryzhik, Table of integrals, series and products, 5th edition, Academic Press, 1994, eq. (3.521.2).
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
E. D. Krupnikov and K. S. Kölbig, Some special cases of the generalized hypergeometric function (q+1)Fq, J. Comp. Appl. Math. 78 (1997) 79-95.
Michael I. Shamos, A catalog of the real numbers, (2007). See p. 594.
FORMULA
Equals Integral_{x=0..oo} x/cosh(x) dx.
Equals 2*A006752.
From Amiram Eldar, Aug 20 2020: (Start)
Equals Integral_{x=0..Pi/2} x/sin(x) dx.
Equals 1 + Integral_{x=0..oo} x * exp(-x) * tanh(x) dx. (End)
Equals 3F2(1/2,1,1;3/2,3/2;1) [Krupnikov]. - R. J. Mathar, May 13 2024
From Stefano Spezia, Nov 12 2024: (Start)
Equals Integral_{x=0..oo} arctan(x)/(x*sqrt(x^2 + 1)) dx = Integral_{x=0..1} K(x^2) dx, where K(x) is the complete elliptic integral of the first kind (see Shamos).
Equals Sum_{k>=0} 2^(2*k)/((2*k + 1)^2*binomial(2*k,k)) (see Finch). (End)
Equals A247685/2. - Hugo Pfoertner, Nov 12 2024
EXAMPLE
1.83193118835443803010920702986476822154...
MAPLE
evalf(2*Catalan) ;
MATHEMATICA
RealDigits[2 Catalan, 10, 100][[1]] (* Bruno Berselli, Feb 21 2013 *)
PROG
(PARI) default(realprecision, 100); 2*Catalan \\ G. C. Greubel, Aug 25 2018
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); 2*Catalan(R); // G. C. Greubel, Aug 25 2018
CROSSREFS
KEYWORD
AUTHOR
R. J. Mathar, Feb 21 2013
STATUS
approved