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A002388 Decimal expansion of Pi^2.
(Formerly M4596 N1961)
33
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)
OFFSET

1,1

COMMENTS

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

REFERENCES

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).

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..20000

Mohammad K. Azarian, Al-Risala al-Muhitiyya: A Summary, (The Treatise on the Circumference), Missouri Journal of Mathematical Sciences, Vol. 22, No. 2, 2010, pp. 64-85.

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

FORMULA

Pi^2 = 11/2 + 16 * sum(k>=2, (1+k-k^3)/(1-k^2)^3 ). [Alexander R. Povolotsky, May 04 2009]

Pi^2 = 3*(sum(n>=1, (2*n+1)^2/(sum(k=1..n, k^3 )) )/4 - 1). [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). [Alexander R. Povolotsky, Aug 13 2011]

Also equals 32*Integral_{0, 1} ArcTan(x)/(1+x^2) dx. [Jean-Fran├žois Alcover, Mar 25 2013]

EXAMPLE

9.869604401089358618834490999876151135313699407240790626413349376220044...

MAPLE

Digits:=100: evalf(Pi^2); # Wesley Ivan Hurt, Jul 13 2014

MATHEMATICA

RealDigits[Pi^2, 10, 111][[1]] (* Robert G. Wilson v *)

PROG

(PARI) { default(realprecision, 20080); x=Pi^2; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b002388.txt", n, " ", d)); } \\ Harry J. Smith, May 31 2009

CROSSREFS

Cf. A102753, A058284.

Sequence in context: A086053 A129269 A094145 * A011116 A106334 A089739

Adjacent sequences:  A002385 A002386 A002387 * A002389 A002390 A002391

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Robert G. Wilson v, Dec 15 2005

STATUS

approved

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Last modified October 1 18:25 EDT 2014. Contains 247522 sequences.