A086468 Decimal expansion of 2*zeta(3)/5.

4, 8, 0, 8, 2, 2, 7, 6, 1, 2, 6, 3, 8, 3, 7, 7, 1, 4, 1, 5, 9, 8, 9, 5, 2, 6, 4, 6, 0, 4, 5, 7, 9, 9, 9, 6, 3, 0, 5, 9, 9, 4, 5, 1, 6, 9, 3, 6, 1, 9, 9, 5, 5, 2, 7, 1, 6, 9, 0, 8, 6, 2, 2, 1, 3, 6, 7, 3, 5, 2, 8, 2, 3, 1, 4, 5, 2, 5, 2, 3, 6, 0, 7, 4, 5, 8, 2, 3, 4, 9, 4, 4, 3, 7, 3, 4, 1, 0, 3, 2, 5, 8

Offset: 0

Author

Eric W. Weisstein, Jul 21 2003

Keywords

• nonn
• cons

Examples

			0.48082276126383771415989526460457999630599451693620...
		

References

• Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch, (1996), 4.1.46.
• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.3, p. 43.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Michael I. Shamos, A catalog of the real numbers, (2007). See p. 446.
• Eric Weisstein's World of Mathematics, Central Binomial Coefficient.

Crossrefs

Cf. A002117, A086465, A086466, A086467.

Programs

Magma

SetDefaultRealField(RealField(250)); L:=RiemannZeta();  2*Evaluate(L,3)/5; // G. C. Greubel, Nov 02 2018

Mathematica

First[RealDigits[N[2*Zeta[3]/5, 100]]] (* Stefano Spezia, Nov 02 2018 *)

PARI

2*zeta(3)/5 \\ Michel Marcus, Nov 02 2018

Formula

Equals Sum_{n>=1} (-1)^(n-1)/(n^3*binomial(2*n,n)).

Equals 2*A002117/5. - R. J. Mathar, Feb 08 2009

Equals (1/10)*Sum_{k>=1} (30*k - 11)/((2*k - 1)*k^3*binomial(2*k,k)^2) (see Finch). - Stefano Spezia, Nov 01 2024