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A245532
Decimal expansion of b_3, a constant associated with the 3rd Du Bois Reymond constant.
1
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
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 * A375392 A324714 A075564
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved