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A221209
Decimal expansion of two times the Catalan constant.
2
1, 8, 3, 1, 9, 3, 1, 1, 8, 8, 3, 5, 4, 4, 3, 8, 0, 3, 0, 1, 0, 9, 2, 0, 7, 0, 2, 9, 8, 6, 4, 7, 6, 8, 2, 2, 1, 5, 4, 8, 2, 9, 8, 7, 4, 8, 5, 6, 3, 3, 4, 4, 2, 6, 8, 5, 3, 2, 9, 9, 6, 2, 3, 9, 2, 4, 3, 5, 2, 6, 0, 3, 9, 5, 5, 2, 5, 0, 9, 5, 3, 8, 9, 5, 8, 7, 1, 3, 0, 2, 5, 8, 5, 2, 2, 3, 0, 2, 1, 2
OFFSET
1,2
REFERENCES
I.S. Gradshteyn and I.M. Ryzhik, Table of integrals, series and products, 5th edition, Academic Press, 1994, eq. (3.521.2).
LINKS
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.
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
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
Cf. A006752.
Sequence in context: A097890 A088453 A019782 * A056030 A364889 A195473
KEYWORD
nonn,cons,easy
AUTHOR
R. J. Mathar, Feb 21 2013
STATUS
approved