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A263353 Decimal expansion of the generalized hypergeometric function 3F2(1/2,1/2,1/2; 3/2,3/2; x) at x=1/2.

%I A263353 #19 Nov 12 2024 17:23:07
%S A263353 1,0,3,2,6,3,1,9,5,5,7,4,4,0,7,1,4,7,2,6,7,7,0,9,3,5,3,3,9,8,1,5,8,5,
%T A263353 8,9,4,7,0,7,3,0,2,8,2,0,4,1,2,2,0,7,6,6,4,8,5,4,0,0,9,8,1,0,5,0,0,2,
%U A263353 3,3,8,7,3,4,6,3,0,7,0,2,0,7,5,0,4,4,8,7,5,0,6,4,3,4,5,4,9,3,3
%N A263353 Decimal expansion of the generalized hypergeometric function 3F2(1/2,1/2,1/2; 3/2,3/2; x) at x=1/2.
%D A263353 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.7.2, p. 55.
%H A263353 G. C. Greubel, <a href="/A263353/b263353.txt">Table of n, a(n) for n = 1..10000</a>
%H A263353 R. J. Mathar, <a href="http://arxiv.org/abs/1207.5845">Yet another table of integrals</a>, arXiv:1207.5845 [math.CA], 2012-2016. Eq. (9.81).
%H A263353 Michael I. Shamos, <a href="http://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf">A catalog of the real numbers</a>, (2007). See p. 65.
%F A263353 Equals (Pi*log(2)/4+Catalan)/sqrt(2) = (A003881 * A002162 + A006752) * A010503.
%F A263353 Equals Sum_{k>=0} binomial(2*k,k)/(2^(3*k)*(2*k + 1)^2) (see Finch). - _Stefano Spezia_, Nov 12 2024
%e A263353 1.032631955744071472677093...
%p A263353 evalf(hypergeom([1/2,1/2,1/2],[3/2,3/2],1/2) );
%t A263353 RealDigits[(Pi*Log[2]/4 + Catalan)/Sqrt[2], 10, 100][[1]] (* _G. C. Greubel_, Aug 25 2018 *)
%o A263353 (PARI) default(realprecision, 100); (Pi*log(2)/4 + Catalan)/sqrt(2) \\ _G. C. Greubel_, Aug 25 2018
%o A263353 (Magma) SetDefaultRealField(RealField(100)); R:=RealField(); (Pi(R)*Log(2)/4 + Catalan(R))/Sqrt(2); // _G. C. Greubel_, Aug 25 2018
%Y A263353 Cf. A002162, A003881, A006752, A010503.
%K A263353 nonn,cons
%O A263353 1,3
%A A263353 _R. J. Mathar_, Oct 16 2015