A256576 Decimal expansion of Ramanujan's constant G(1) = Sum_{r>=1} 1/(2r^3)*(1 + 1/3 + ... + 1/(2r-1)).

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

Offset

0,2

Links

Table of n, a(n) for n=0..99.

Marc-Antoine Coppo and Bernard Candelpergher, Inverse binomial series and values of Arakawa-Kaneko zeta functions, J. Number Theory 150 (2015) 98-119 eq. (25).

R. Sitaramachandrarao, A Formula of S. Ramanujan , Journal of Number Theory 25, 1-19 (1987)

Formula

G(1) = Pi^4/480 - (1/4)*Sum_{r>=2} (-1)^r*H(r-1,2)/r^2, where H(n,m) is the n-th harmonic number of order m.

F(1) = 7*Zeta(3)/16 = Sum_{r>=1} (1+1/3+1/5+..+1/(2r-1))/r^2 = 0.525899895... [Coppo] - R. J. Mathar, Jun 13 2024

Example

0.1622719394714833907153595518080712064734997514...

Mathematica

digits = 100; G1 = NSum[(1/(2*r)^3)*(1/2*(EulerGamma + Log[4]) + 1/2*PolyGamma[ 1/2+r]), {r, 1, Infinity}, WorkingPrecision -> digits+10, NSumTerms -> 40, Method -> {"NIntegrate", "MaxRecursion" -> 10}]; RealDigits[G1, 10, digits] // First

Crossrefs

Sequence in context: A172439 A169684 A259838 * A201674 A093497 A092138

Adjacent sequences: A256573 A256574 A256575 * A256577 A256578 A256579

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 02 2015

Status

approved