

A193887


Decimal expansion of Pi * sqrt(2)/8.


5



5, 5, 5, 3, 6, 0, 3, 6, 7, 2, 6, 9, 7, 9, 5, 7, 8, 0, 8, 7, 6, 9, 8, 5, 1, 2, 3, 7, 5, 7, 5, 8, 6, 7, 1, 2, 3, 2, 6, 8, 2, 7, 7, 1, 1, 1, 7, 1, 9, 6, 1, 2, 7, 7, 8, 8, 5, 6, 7, 4, 4, 5, 0, 8, 6, 9, 5, 5, 4, 3, 4, 9, 1, 3, 7, 4
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OFFSET

0,1


COMMENTS

This number arises as an addend in one way of giving the closed form of sum(k>=0, (1)^k/(4*k + 1) ), for example, in Spiegel et al. (2009).


REFERENCES

Murray R. Spiegel, Seymour Lipschutz, John Liu. Mathematical Handbook of Formulas and Tables, 3rd Ed. Schaum's Outline Series. New York: McGrawHill (2009): p. 135, equation 21.17


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000
Piotr Garbaczewski, Vladimir Stephanovich, Semigroup modeling of confined Levy flights" arXiv:1106.1530 [condmat.statmech], 2011, p. 8, equation 40.


FORMULA

c = Pi/(4*sqrt(2)).
c = Sum_{k >= 0} (1)^k * (4*k + 2)/((4*k + 1)*(4*k + 3)).  Peter Bala, Sep 21 2016


EXAMPLE

0.55536036726979578088...


MATHEMATICA

RealDigits[(Pi Sqrt[2])/8, 10, 100][[1]]


PROG

(PARI) Pi*sqrt(2)/8 \\ G. C. Greubel, Feb 02 2018
(MAGMA) R:= RealField(); Pi(R)*Sqrt(2)/8; // G. C. Greubel, Feb 02 2018


CROSSREFS

Cf. A181048, A063448, A247719, A093954, A244976.
Sequence in context: A173602 A054245 A302552 * A196998 A232614 A254609
Adjacent sequences: A193884 A193885 A193886 * A193888 A193889 A193890


KEYWORD

nonn,cons


AUTHOR

Alonso del Arte, Aug 07 2011


STATUS

approved



