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A072691 Decimal expansion of Pi^2/12. 15
8, 2, 2, 4, 6, 7, 0, 3, 3, 4, 2, 4, 1, 1, 3, 2, 1, 8, 2, 3, 6, 2, 0, 7, 5, 8, 3, 3, 2, 3, 0, 1, 2, 5, 9, 4, 6, 0, 9, 4, 7, 4, 9, 5, 0, 6, 0, 3, 3, 9, 9, 2, 1, 8, 8, 6, 7, 7, 7, 9, 1, 1, 4, 6, 8, 5, 0, 0, 3, 7, 3, 5, 2, 0, 1, 6, 0, 0, 4, 3, 6, 9, 1, 6, 8, 1, 4, 4, 5, 0, 3, 0, 9, 8, 7, 9, 3, 5, 2, 6, 5, 2, 0, 0, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Also -dilogarithm(-1). - Rick L. Shepherd, Jul 21 2004

Also zeta(1,1), the double zeta-function with both arguments equal to 1. - R. J. Mathar, Oct 10 2011

Also zeta(2)/2. [Jean-François Alcover, May 17 2013]

REFERENCES

C. C. Clawson, The Beauty and Magic of Numbers. New York: Plenum Press (1996): 98

Jolley, Summation of Series, Dover (1961) eq. (234) page 44.

LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Dilogarithm

FORMULA

Equals 1/(1*2)+ 1/(2*4) + 1/(3*6)+ 1/(4*8)+ ... [Jolley]

Sum_{n>=1} ((-1)^(n+1))/n^2 [Clawson]. - Alonso del Arte, Aug 15 2012

Equals integral(x=0..1) log((1+x^3)/(1-x^3))/x dx. [Bruno Berselli, May 13 2013]

Equals integral(x=1..2) log(x)/(x-1) dx. [Jean-François Alcover, May 17 2013]

EXAMPLE

0.822467033424113218236207583323... = A013661/2.

MATHEMATICA

RealDigits[Pi^2/12, 10, 105][[1]] (* Robert G. Wilson v *)

PROG

(PARI) zeta(2)/2 \\ Michel Marcus, Sep 08 2014

CROSSREFS

Cf. A072692 (Pi^2/12 is in asymptotic formula related to sigma(n), A000203).

Cf. A113319: sum( i>=0, 1/(i^2+1) ); A232883: sum( i>=0, 1/(2*i^2+1) ).

Sequence in context: A138997 A248498 A133918 * A021928 A185111 A086058

Adjacent sequences:  A072688 A072689 A072690 * A072692 A072693 A072694

KEYWORD

nonn,cons

AUTHOR

Rick L. Shepherd, Jul 02 2002

STATUS

approved

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Last modified November 28 12:57 EST 2014. Contains 250359 sequences.