A245532 Decimal expansion of b_3, a constant associated with the 3rd Du Bois Reymond constant.

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

Offset

0,3

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.12 Du Bois Reymond Constants, pp. 238-239.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, du Bois-Reymond Constants.

Formula

b_3 = (-1/4)*(e^3 - 3*e - 12).

Equals 2*sum((-1)^(n+1)/(1+xi(n)^2)^(3/2), (n=1..infinity)), where xi(n) is the n-th positive solution to tan(x)=x.

Example

0.017327140547366991288083189869067399070958360636432145130492163368346...

Maple

Digits:=100: evalf((-1/4)*(exp(3)-3*exp(1)-12)); # Wesley Ivan Hurt, Jul 26 2014

Mathematica

b3 = (-1/4)*(E^3 - 3*E - 12); Join[{0}, RealDigits[b3, 10, 101] // First]

Prog

(PARI) (12+3*exp(1)-exp(3))/4 \\ Charles R Greathouse IV, Jul 25 2014

Crossrefs

Cf. A224196.

Sequence in context: A309387 A298530 A243377 * A324714 A075564 A303670

Adjacent sequences: A245529 A245530 A245531 * A245533 A245534 A245535

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jul 25 2014

Status

approved