A374641 -id:A374641 - cp's OEIS frontend

A374642 Decimal expansion of log(1111111111/387420489).

1, 0, 5, 3, 6, 0, 5, 1, 5, 6, 4, 7, 8, 2, 6, 3, 0, 1, 2, 2, 7, 0, 0, 0, 9, 8, 0, 8, 3, 9, 2, 7, 9, 4, 6, 4, 9, 7, 2, 7, 8, 4, 5, 3, 9, 6, 4, 9, 9, 4, 0, 5, 3, 9, 2, 3, 0, 6, 0, 5, 8, 8, 3, 6, 9, 2, 5, 8, 4, 0, 2, 1, 8, 1, 1, 5, 6, 3, 1, 1, 7, 7, 9, 2, 3, 3, 7, 1, 2, 4

Offset: 1

Paolo Xausa, Jul 15 2024

			1.053605156478263012270009808392794649727845396499...

Paolo Xausa, Table of n, a(n) for n = 1..10000
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).
Index entries for transcendental numbers

Cf. A374641, A374643, A374644.

First[RealDigits[Log[1111111111/387420489], 10, 100]]

log(1111111111/387420489) \\ Charles R Greathouse IV, Nov 21 2024

Equals 10^(-8)*Sum_{k >= 0} 1/(10^(10*k))*(Sum{j = 1..9} 10^(9-j)/(10*k + j)). See Bailey and Crandall (2001), p. 185.

A374643 Decimal expansion of 12*Li_2(1/2), where Li_2(z) is the dilogarithm function.

Original entry on oeis.org

6, 9, 8, 6, 8, 8, 6, 3, 1, 7, 5, 8, 0, 1, 5, 0, 0, 7, 0, 8, 3, 1, 8, 7, 5, 8, 4, 1, 9, 1, 6, 1, 6, 1, 3, 0, 4, 9, 3, 0, 3, 8, 1, 6, 9, 7, 6, 7, 3, 5, 1, 7, 1, 0, 5, 2, 1, 2, 1, 6, 4, 5, 7, 4, 4, 7, 8, 0, 5, 2, 5, 2, 8, 8, 6, 0, 1, 9, 8, 4, 0, 9, 8, 0, 2, 0, 8, 3, 8, 2

Offset: 1

Paolo Xausa, Jul 15 2024

			6.98688631758015007083187584191616130493038169767...

Paolo Xausa, Table of n, a(n) for n = 1..10000
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, Dilogarithm.
Wikipedia, Dilogarithm.

Cf. A002388, A076788, A253191, A374641, A374642, A374644.

First[RealDigits[12*PolyLog[2, 1/2], 10, 100]]

Equals 12*A076788.

Equals Pi^2 - 6*log(2)^2 = A002388 - 6*A253191 = 12*Sum_{k >= 1} 1/((2^k)*(k^2)). See Bailey et al. (1997), eq. 2.7, p. 906 and Bailey and Crandall (2001), p. 184.

A374644 Decimal expansion of 24*Li_3(1/2), where Li_m(z) is the polylogarithm function.

Original entry on oeis.org

1, 2, 8, 9, 3, 1, 1, 6, 6, 4, 6, 5, 9, 2, 9, 6, 4, 8, 2, 2, 5, 7, 4, 9, 5, 7, 4, 1, 4, 2, 7, 9, 1, 7, 9, 8, 4, 0, 0, 8, 9, 6, 5, 9, 9, 8, 4, 1, 6, 9, 0, 7, 6, 0, 9, 6, 5, 5, 4, 2, 8, 6, 3, 3, 7, 2, 3, 9, 7, 7, 7, 9, 4, 2, 0, 8, 3, 3, 2, 1, 5, 3, 5, 9, 2, 9, 8, 9, 6, 6

Offset: 2

Paolo Xausa, Jul 15 2024

			12.893116646592964822574957414279179840089659984...

Paolo Xausa, Table of n, a(n) for n = 2..10000
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.

Cf. A002117, A002162, A002388, A099217, A352769, A374641, A374642, A374643.

First[RealDigits[24*PolyLog[3, 1/2], 10, 100]]

Equals 24*A099217.

Equals 4*log(2)^3 + 21*zeta(3) - 2*Pi^2*log(2) = 4*A002162^3 + 21*A002117 - 2*A352769 = 24*Sum_{k >= 1} 1/((2^k)*(k^3)). See Bailey and Crandall (2001), p. 184.

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A374642 Decimal expansion of log(1111111111/387420489).

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A374643 Decimal expansion of 12*Li_2(1/2), where Li_2(z) is the dilogarithm function.

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A374644 Decimal expansion of 24*Li_3(1/2), where Li_m(z) is the polylogarithm function.

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