

A248914


Decimal expansion of L = integral_{0..1} 1/(12t^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
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OFFSET

1,2


REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.6 Sobolev Isoperimetric Constants.


LINKS

Table of n, a(n) for n=1..101.
David W. Boyd, Best constants in a class of integral inequalities, Pacific J. Math. Volume 30, Number 2 (1969), 367383
Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 31.
Steven R. Finch, Errata and Addenda to Mathematical Constants, January 22, 2016. [Cached copy, with permission of the author]


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

Cf. A242440, A244263, A244347, A244354, A245292, A246859.
Sequence in context: A085655 A153615 A281531 * A246686 A048649 A200008
Adjacent sequences: A248911 A248912 A248913 * A248915 A248916 A248917


KEYWORD

nonn,cons,easy


AUTHOR

JeanFrançois Alcover, Oct 16 2014


STATUS

approved



