

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
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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 Lfunction of modulus m=8 at argument s=1 for the nonprincipal 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. [JeanFrançois Alcover, Mar 28 2013]
Also equals integral_{0, infinity} 1/(x^4+1) dx. [JeanFrançois 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 Lseries 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=(xd)*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



