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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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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
W. E. Mansell, Tables of Natural and Common Logarithms. Royal Society Mathematical Tables, Vol. 8, Cambridge Univ. Press, 1964, p. XVIII.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,20000
Index entries for sequences related to the number Pi
D. H. Bailey and J. M. Borwein, Experimental Mathematics: Examples, Methods and Implications
S. Plouffe, Pi^2 to 10000 digits
S. Plouffe, Plouffe's Inverter, Pi^2 to 10000 digits
N. D. Elkies, Why is (pi)^2 so close to 10?
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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]
Adjacent sequences: A002385 A002386 A002387 this_sequence A002389 A002390 A002391
Sequence in context: A086053 A129269 A094145 this_sequence A011116 A106334 A089739
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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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