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

Author

Jean-François Alcover, Jul 25 2014

Keywords

• nonn
• cons
• easy

Examples

			0.017327140547366991288083189869067399070958360636432145130492163368346...
		

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.

Crossrefs

Cf. A224196.

Programs

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]

PARI

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

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.