A374642 -id:A374642 - cp's OEIS frontend

A374641 Decimal expansion of log(9/10), negated.

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

Paolo Xausa, Jul 15 2024

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

			0.105360515657826301227500980839312798306120372983...

Paolo Xausa, Table of n, a(n) for n = 0..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, Polylogarithm.
Wikipedia, Polylogarithm.
Index entries for transcendental numbers

Cf. A126431, A374642, A374643, A374644.

Mathematica
```
First[RealDigits[Log[9/10], 10, 100]]
```

-log(.9) \\ Charles R Greathouse IV, Jul 17 2024

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.

Equals Integral_{x=0..1} (x^(1/3) - x^(1/5))/log(x) dx. - Kritsada Moomuang, May 27 2025

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.

cp's OEIS Frontend

A374641 Decimal expansion of log(9/10), negated.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula