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A248914
Decimal expansion of L = integral_{0..1} 1/(1-2t^2/3) dt, an auxiliary constant associated with one of the integral inequalities studied by David Boyd.
0
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
1,2
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
FORMULA
L = sqrt(3/2]*arctanh(sqrt(2/3)).
K = A246859 = 2/(L+1)^2.
EXAMPLE
1.40382196515535516573036373889961027748003532830665702207...
MATHEMATICA
RealDigits[Sqrt[3/2]*ArcTanh[Sqrt[2/3]], 10, 101] // First
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved