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

1,3

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.

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

Example

1.032631955744071472677093...

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 *)

Prog

(PARI) default(realprecision, 100); (Pi*log(2)/4 + Catalan)/sqrt(2) \\ G. C. Greubel, Aug 25 2018
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); (Pi(R)*Log(2)/4 + Catalan(R))/Sqrt(2); // G. C. Greubel, Aug 25 2018

Crossrefs

Cf. A002162, A003881, A006752, A010503.

Sequence in context: A078589 A077880 A198930 * A248945 A131969 A058971

Adjacent sequences: A263350 A263351 A263352 * A263354 A263355 A263356

Keyword

nonn,cons

Author

R. J. Mathar, Oct 16 2015

Status

approved