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A093954 Decimal expansion of Pi/(2*sqrt(2)). 7
1, 1, 1, 0, 7, 2, 0, 7, 3, 4, 5, 3, 9, 5, 9, 1, 5, 6, 1, 7, 5, 3, 9, 7, 0, 2, 4, 7, 5, 1, 5, 1, 7, 3, 4, 2, 4, 6, 5, 3, 6, 5, 5, 4, 2, 2, 3, 4, 3, 9, 2, 2, 5, 5, 5, 7, 7, 1, 3, 4, 8, 9, 0, 1, 7, 3, 9, 1, 0, 8, 6, 9, 8, 2, 7, 4, 8, 6, 8, 4, 7, 7, 6, 4, 3, 8, 3, 1, 7, 3, 3, 6, 9, 1, 1, 9, 1, 3, 0, 9, 3, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The value is the length Pi*sqrt(2)/4 of the diagonal in the square with side length Pi/4 = sum_{n>=0}  (-1)^n/(2n+1) = A003881. The area of the circumcircle of this square is Pi*(Pi*sqrt(2)/8)^2 = Pi^3/32 = A153071. - Eric Desbiaux, Jan 18 2009

This is the value of the Dirichlet L-function of modulus m=8 at argument s=1 for the non-principal character (1,0,1,0,-1,0,-1,0). See arXiv:1008.2547. - R. J. Mathar, Mar 22 2011

Also equals the Fresnel integrals integral_{0, infinity} sin(x^2) dx or integral_{0, infinity} cos(x^2) dx. [Jean-François Alcover, Mar 28 2013]

Also equals integral_{0, infinity} 1/(x^4+1) dx. [Jean-François Alcover, Apr 29 2013]

REFERENCES

George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 149.

Jolley, Summation of Series, Dover (1961) eq 76 page 16.

LINKS

Harry J. Smith, Table of n, a(n) for n=1,...,20000

R. J. Mathar, Table of Dirichlet L-series and prime zeta modulo functions for small moduli, arXiv:1008.2547, table 7 and section 2.2, value of L(m=8,r=4,s=1).

Eric Weisstein's World of Mathematics, Bifoliate

EXAMPLE

1.11072073... = 1/A112628.

PROG

(PARI) { default(realprecision, 20080); x=Pi*sqrt(2)/4; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b093954.txt", n, " ", d)); } [From Harry J. Smith, Jun 17 2009]

CROSSREFS

Cf. A161684 Continued fraction. [From Harry J. Smith, Jun 17 2009]

Sequence in context: A232812 A245740 A236565 * A177703 A200338 A153589

Adjacent sequences:  A093951 A093952 A093953 * A093955 A093956 A093957

KEYWORD

nonn,cons,easy

AUTHOR

Eric W. Weisstein, Apr 19, 2004

STATUS

approved

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Last modified September 19 05:32 EDT 2014. Contains 246972 sequences.