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A193887

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

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: McGraw-Hill (2009): p. 135, equation 21.17

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

Piotr Garbaczewski and Vladimir Stephanovich, Semigroup modeling of confined Levy flights, arXiv:1106.1530 [cond-mat.stat-mech], 2011, p. 8, equation 40.

Index entries for transcendental numbers

FORMULA

Equals Pi/(4*sqrt(2)).

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

From Amiram Eldar, Aug 15 2020: (Start)

Equals Integral_{x=0..oo} 1/(x^2 + 8) dx.

Equals Integral_{x=0..oo} 1/(8*x^2 + 1) dx.

Equals Integral_{x=0..oo} 1/(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7) dx. (End)

EXAMPLE

0.55536036726979578088...

MATHEMATICA

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