A248914 Decimal expansion of L = Integral_{t=0..1} 1/(1-2t^2/3) dt, an auxiliary constant associated with one of the integral inequalities studied by David Boyd.
1, 4, 0, 3, 8, 2, 1, 9, 6, 5, 1, 5, 5, 3, 5, 5, 1, 6, 5, 7, 3, 0, 3, 6, 3, 7, 3, 8, 8, 9, 9, 6, 1, 0, 2, 7, 7, 4, 8, 0, 0, 3, 5, 3, 2, 8, 3, 0, 6, 6, 5, 7, 0, 2, 2, 0, 7, 0, 0, 0, 4, 5, 5, 7, 2, 5, 8, 4, 8, 6, 4, 0, 8, 1, 3, 7, 8, 1, 3, 4, 8, 0, 0, 2, 3, 0, 0, 2, 9, 0, 8, 4, 7, 6, 6, 2, 7, 4, 4, 9, 2
Offset: 1
Examples
1.40382196515535516573036373889961027748003532830665702207...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.6 Sobolev Isoperimetric Constants.
Links
- David W. Boyd, Best constants in a class of integral inequalities, Pacific J. Math. Volume 30, Number 2 (1969), 367-383
- Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 31.
Programs
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Mathematica
RealDigits[Sqrt[3/2]*ArcTanh[Sqrt[2/3]], 10, 101] // First
Formula
L = sqrt(3/2)*arctanh(sqrt(2/3)).
K = A246859 = 2/(L+1)^2.