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

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, 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, 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

Offset: 1

Author

R. J. Mathar, Oct 16 2015

Keywords

• nonn
• cons

Examples

			1.032631955744071472677093...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.7.2, p. 55.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• R. J. Mathar, Yet another table of integrals, arXiv:1207.5845 [math.CA], 2012-2016. Eq. (9.81).
• Michael I. Shamos, A catalog of the real numbers, (2007). See p. 65.

Crossrefs

Cf. A002162, A003881, A006752, A010503.

Programs

Magma

SetDefaultRealField(RealField(100)); R:=RealField(); (Pi(R)*Log(2)/4 + Catalan(R))/Sqrt(2); // G. C. Greubel, Aug 25 2018

Maple

evalf(hypergeom([1/2,1/2,1/2],[3/2,3/2],1/2) );

Mathematica

RealDigits[(Pi*Log[2]/4 + Catalan)/Sqrt[2], 10, 100][[1]] (* G. C. Greubel, Aug 25 2018 *)

PARI

default(realprecision, 100); (Pi*log(2)/4 + Catalan)/sqrt(2) \\ G. C. Greubel, Aug 25 2018

Formula

Equals (Pi*log(2)/4+Catalan)/sqrt(2) = (A003881 * A002162 + A006752) * A010503.

Equals Sum_{k>=0} binomial(2*k,k)/(2^(3*k)*(2*k + 1)^2) (see Finch). - Stefano Spezia, Nov 12 2024