A086730 Decimal expansion of sum(1/(6*m+4)^2,m=0..infinity).

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

Offset

0,2

References

L. Fejes Toth, Lagerungen in der Ebene, auf der Kugel und im Raum, 2nd. ed., Springer-Verlag, Berlin, Heidelberg 1972; see p. 213.

Links

Table of n, a(n) for n=0..98.

Formula

.085107650259964... = Psi'(2/3)/36 where Psi'(x) denotes the first derivative of the digamma function - R. Piyo (nagoya314(AT)yahoo.com), Dec 12 2004

8*Zeta(2)/9 = A214550 +4*(this constant) with Zeta(2) = A013661. - R. J. Mathar, Sep 15 2012

Example

0.085107650259964...

Mathematica

RealDigits[ PolyGamma[1, 2/3]/36, 10, 98] // First // Prepend[#, 0]& (* Jean-François Alcover, Feb 12 2013 *)

Prog

(PARI) psi'(2/3)/36 \\ Charles R Greathouse IV, Jul 19 2013

Crossrefs

Cf. A086722-A086731.

Sequence in context: A143347 A073448 A073745 * A249449 A357466 A334496

Adjacent sequences: A086727 A086728 A086729 * A086731 A086732 A086733

Keyword

nonn,cons

Author

N. J. A. Sloane, Jul 31 2003

Status

approved