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A002388
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Decimal expansion of Pi^2.
(Formerly M4596 N1961)
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31
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9, 8, 6, 9, 6, 0, 4, 4, 0, 1, 0, 8, 9, 3, 5, 8, 6, 1, 8, 8, 3, 4, 4, 9, 0, 9, 9, 9, 8, 7, 6, 1, 5, 1, 1, 3, 5, 3, 1, 3, 6, 9, 9, 4, 0, 7, 2, 4, 0, 7, 9, 0, 6, 2, 6, 4, 1, 3, 3, 4, 9, 3, 7, 6, 2, 2, 0, 0, 4, 4, 8, 2, 2, 4, 1, 9, 2, 0, 5, 2, 4, 3, 0, 0, 1, 7, 7, 3, 4, 0, 3, 7, 1, 8, 5, 5, 2, 2, 3, 1, 8, 2, 4, 0, 2
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Also equals the volume of revolution of the sine or cosine curve for one full period,Integral_{0,2Pi} Sin(x)^2 dx. - Robert G. Wilson v Dec 15 2005. - Robert G. Wilson v, Dec 15 2005
Also equals 32*Integral_{0, 1} ArcTan(x)/(1+x^2) dx [Jean-François Alcover, Mar 25 2013]
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REFERENCES
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Mohammad K. Azarian, Al-Risala al-Muhitiyya: A Summary, Missouri Journal of Mathematical Sciences, Vol. 22, No. 2, 2010, pp. 64-85.
W. E. Mansell, Tables of Natural and Common Logarithms. Royal Society Mathematical Tables, Vol. 8, Cambridge Univ. Press, 1964, p. XVIII.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,20000
D. H. Bailey and J. M. Borwein, Experimental Mathematics: Examples, Methods and Implications
N. D. Elkies, Why is (pi)^2 so close to 10?
_Simon Plouffe_, Pi^2 to 10000 digits
_Simon Plouffe_, Plouffe's Inverter, Pi^2 to 10000 digits
Index entries for sequences related to the number Pi
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FORMULA
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Pi^2 = 11/2 + 16 * sum(k>=2, (1+k-k^3)/(1-k^2)^3 ) [From Alexander R. Povolotsky, May 04 2009]
Pi^2 = 3*(sum(n>=1, (2*n+1)^2/(sum(k=1..n, k^3 )) )/4 - 1) [From Alexander R. Povolotsky, Jan 14 2011]
Pi^2 = 3/2*(sum(n>=1, (7*n^2+2*n-2)/(2*n^2-1)/(n+1)^5 ) -zeta(3) -3*zeta(5)+22-7*polygamma(0,1-1/sqrt(2)) +5*sqrt(2)*polygamma(0,1-1/sqrt(2)) -7*polygamma(0,1+1/sqrt(2)) -5*sqrt(2)*polygamma(0,1+1/sqrt(2)) -14*EulerGamma) [From Alexander R. Povolotsky, Aug 13 2011]
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EXAMPLE
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9.869604401089358618834490999876151135313699407240790626413349376220044... [From Harry J. Smith, May 31 2009]
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MAPLE
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Pi^2 = 11/2 + 16 * sum(k>=2, (1+k-k^3)/(1-k^2)^3 ) [From Alexander R. Povolotsky, May 04 2009]
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MATHEMATICA
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RealDigits[Pi^2, 10, 111][[1]] (* Robert G. Wilson v *)
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PROG
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(PARI) { default(realprecision, 20080); x=Pi^2; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b002388.txt", n, " ", d)); } [From Harry J. Smith, May 31 2009]
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CROSSREFS
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Cf. A102753.
Cf. A058284 Continued fraction. [From Harry J. Smith, May 31 2009]
Sequence in context: A086053 A129269 A094145 * A011116 A106334 A089739
Adjacent sequences: A002385 A002386 A002387 * A002389 A002390 A002391
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KEYWORD
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nonn,cons
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Robert G. Wilson v, Dec 15 2005
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STATUS
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approved
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