A245532 - OEIS

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

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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