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A069998
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Decimal expansion of sqrt(Pi/2).
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9
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1, 2, 5, 3, 3, 1, 4, 1, 3, 7, 3, 1, 5, 5, 0, 0, 2, 5, 1, 2, 0, 7, 8, 8, 2, 6, 4, 2, 4, 0, 5, 5, 2, 2, 6, 2, 6, 5, 0, 3, 4, 9, 3, 3, 7, 0, 3, 0, 4, 9, 6, 9, 1, 5, 8, 3, 1, 4, 9, 6, 1, 7, 8, 8, 1, 7, 1, 1, 4, 6, 8, 2, 7, 3, 0, 3, 9, 2, 0, 9, 8, 7, 4, 7, 3, 2, 9, 7, 9, 1, 9, 1, 8, 9, 0, 2, 8, 6, 3, 3, 0, 5, 8, 0, 0, 4
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OFFSET
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1,2
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COMMENTS
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This constant, sqrt(Pi/2), appears in one of the formulations of the Birthday Problem: An asymptotic expansion of the expected value for the average number of people required to find a pair having the same birthday out of k possible birthdays is sqrt(Pi/2)*sqrt(k) + 2/3 + 1/12*sqrt(Pi/2)*sqrt(1/k) - 4/135*1/k + ... found by the Indian mathematician Srinivasa Ramanujan (1887-1920). - Martin Renner, Sep 14 2016
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 1..5000
P. Flajolet, P. J. Grabner, P. Kirschenhofer and H. Prodinger, On Ramanujan's Q-Function, Journal of Computational and Applied Mathematics 58 (1995), 103-116.
I. S. Gradsteyn and I. M. Ryzhik, Table of integrals, series and products, (1980), page 420 (formulas 3.757.1, 3.757.2).
Index entries for transcendental numbers
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FORMULA
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From A.H.M. Smeets, Sep 22 2018: (Start)
Equals Integral_{x >= 0} sin(x)/sqrt(x) dx [see Gradsteyn and Ryzhik].
Equals Integral_{x >= 0} cos(x)/sqrt(x) dx [see Gradsteyn and Ryzhik]. (End)
Equals Integral_{x>=0} (sin(x)-x*cos(x))/x^(3/2) dx. - Amiram Eldar, May 08 2021
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EXAMPLE
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Sqrt(Pi/2) = 1.253314137315500251207882642... - Wesley Ivan Hurt, Sep 22 2016
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MAPLE
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Digits:=100: evalf(sqrt(Pi/2)); # Wesley Ivan Hurt, Sep 22 2016
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MATHEMATICA
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RealDigits[Sqrt[Pi/2], 10, 120][[1]] (* Harvey P. Dale, Jul 24 2012 *)
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PROG
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(PARI) sqrt(Pi/2) \\ G. C. Greubel, Jan 09 2017
(PARI) intnum(x=0, [oo, -I], sin(x)/sqrt(x)) \\ Gheorghe Coserea, Sep 23 2018
(PARI) intnum(x=[0, -1/2], [oo, I], cos(x)/sqrt(x)) \\ Gheorghe Coserea, Sep 23 2018
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CROSSREFS
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Cf. A064619.
Sequence in context: A212887 A163766 A004200 * A162405 A141637 A185581
Adjacent sequences: A069995 A069996 A069997 * A069999 A070000 A070001
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KEYWORD
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cons,easy,nonn
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AUTHOR
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Benoit Cloitre, May 01 2002
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STATUS
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approved
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