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A072691 Decimal expansion of Pi^2/12. 37
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

Lim_{n->infinity} A244583(n)/prime(n)^2. See A244583 for details. - Richard R. Forberg, Jan 04 2015

REFERENCES

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

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.11 p. 126 and section 8.5 p. 501.

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

(PARI) -dilog(-1) \\ Charles R Greathouse IV, Apr 17 2015

(PARI) Pi^2/12 \\ Charles R Greathouse IV, Apr 17 2015

(PARI) zetamult([1, 1]) \\ Charles R Greathouse IV, Apr 17 2015

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 December 8 10:49 EST 2016. Contains 278939 sequences.