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Search: id:A002388
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| A002388 |
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Decimal expansion of pi^2.
(Formerly M4596 N1961)
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+0
16
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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; cons; graph; listen)
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OFFSET
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1,1
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COMMENT
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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 (rgwv(at)rgwv.com), Dec 15 2005
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REFERENCES
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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?
S. Plouffe, Pi^2 to 10000 digits
S. 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((1+k-k^3)/(1-k^2)^3,k=2...infinity) [From Alexander R. Povolotsky (pevnev(AT)juno.com), May 04 2009]
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EXAMPLE
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9.8696044010893586188344909998761511353136994072407906264133493762...
9.869604401089358618834490999876151135313699407240790626413349376220044... [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 31 2009]
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MAPLE
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Pi^2 = 11/2 + 16 * sum((1+k-k^3)/(1-k^2)^3, k=2...infinity) [From Alexander R. Povolotsky (pevnev(AT)juno.com), 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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PROGRAM
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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 (hjsmithh(AT)sbcglobal.net), May 31 2009]
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CROSSREFS
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Cf. A102753.
Cf. A058284 Continued fraction. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 31 2009]
Sequence in context: A086053 A129269 A094145 this_sequence A011116 A106334 A089739
Adjacent sequences: A002385 A002386 A002387 this_sequence 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 (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Dec 15 2005
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