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A374641
Decimal expansion of log(9/10), negated.
4
1, 0, 5, 3, 6, 0, 5, 1, 5, 6, 5, 7, 8, 2, 6, 3, 0, 1, 2, 2, 7, 5, 0, 0, 9, 8, 0, 8, 3, 9, 3, 1, 2, 7, 9, 8, 3, 0, 6, 1, 2, 0, 3, 7, 2, 9, 8, 3, 2, 7, 4, 0, 7, 2, 5, 6, 3, 9, 3, 9, 2, 3, 3, 6, 9, 2, 5, 8, 4, 0, 2, 3, 2, 4, 0, 1, 3, 4, 5, 4, 6, 4, 8, 8, 7, 6, 5, 6, 9, 5
OFFSET
0,3
COMMENTS
Bailey et al. (1997) use Li_1(1/10) (see Formula section) to compute the ten billionth digit of this constant.
Bailey and Crandall (2001), p. 185, present this constant as an example of an irrational number that, provided their "Hypothesis A" (p. 176) is true, is normal to base 10.
Also decimal expansion of log(10/9). - Charles R Greathouse IV, Jul 17 2024
LINKS
David Bailey, Peter Borwein, and Simon Plouffe, On the Rapid Computation of Various Polylogarithmic Constants, Mathematics of Computation, Vol. 66, No. 218, April 1997, pp. 903-913.
David H. Bailey and Richard E. Crandall, On the Random Character of Fundamental Constant Expansions, Experimental Mathematics, Vol. 10 (2001), Issue 2, pp. 175-190 (preprint draft).
Eric Weisstein's MathWorld, Polylogarithm.
Wikipedia, Polylogarithm.
FORMULA
Equals Li_1(1/10) = Sum_{k >= 1} 1/(k*10^k), where Li_m(z) is the polylogarithm function. See Bailey et al. (1997), p. 909 and Bailey and Crandall (2001), p. 185.
EXAMPLE
0.105360515657826301227500980839312798306120372983...
MATHEMATICA
First[RealDigits[Log[9/10], 10, 100]]
PROG
(PARI) -log(.9) \\ Charles R Greathouse IV, Jul 17 2024
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Paolo Xausa, Jul 15 2024
STATUS
approved