A099217 -id:A099217 - cp's OEIS frontend

A099218 Decimal expansion of Li_4(1/2).

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

Offset: 0

Benoit Cloitre, Oct 06 2004

Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch, (1996), Section 1.3.2.

G. Rutledge, R. D. Douglass, Table of definite integrals, Am. Math. Monthly 45 (8) (1938) 525-530, eq. (22).

Cf. A076788, A099217, A099219, A099220, A099221, A099222, A099223, A099224.

polylog(4,1/2) ; evalf(%) ; # R. J. Mathar, Feb 15 2013

RealDigits[ N[ PolyLog[4, 1/2], 104]][[1]] (* Jean-François Alcover, Nov 07 2012 *)

polylog(4,1/2) \\ Charles R Greathouse IV, Jul 14 2014

Li_4(1/2)=sum(k>0, 1/2^k/k^4)=0.5174790616738993863...

Leading zero removed, formula value corrected by R. J. Mathar, Feb 05 2009

A099219 Decimal expansion of Li_5(1/2).

Original entry on oeis.org

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

Offset: 0

Benoit Cloitre, Oct 06 2004

			0.50840057924...

Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch (1996), Section 1.3.2.

Cf. A076788, A099217, A099218, A099220, A099221, A099222, A099223, A099224.

polylog(5,1/2) ; evalf(%) ; # R. J. Mathar, Feb 15 2013

RealDigits[N[PolyLog[5, 1/2], 104]][[1]] (* Jean-François Alcover, Nov 07 2012 *)

polylog(5,1/2) \\ Charles R Greathouse IV, Jul 14 2014

Li_5(1/2) = Sum_{k>0} 1/2^k/k^5.

A099220 Decimal expansion of Li_6(1/2).

Original entry on oeis.org

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

Offset: 0

Benoit Cloitre, Oct 06 2004

Cf. A076788, A099217, A099218, A099219, A099221, A099222, A099223, A099224.

RealDigits[ N[ PolyLog[6, 1/2], 105]][[1]] (* Jean-François Alcover, Nov 07 2012 *)

polylog(6,1/2) \\ Charles R Greathouse IV, Jul 14 2014

Li_6(1/2)=sum(k>0, 1/2^k/k^6)=0.5040953978...

A099221 Decimal expansion of Li_7(1/2).

Original entry on oeis.org

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

Offset: 0

Benoit Cloitre, Oct 06 2004

Cf. A076788, A099217, A099218, A099219, A099220, A099222, A099223, A099224.

RealDigits[ N[ PolyLog[7, 1/2], 105]][[1]] (* Jean-François Alcover, Nov 07 2012 *)

polylog(7,1/2) \\ Charles R Greathouse IV, Jul 14 2014

Li_7(1/2)=sum(k>0, 1/2^k/k^7)=0.50201456332470849456....

Formula value corrected and leading zero removed by R. J. Mathar, Feb 05 2009

A099222 Decimal expansion of Li_8(1/2).

Original entry on oeis.org

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

Offset: 0

Benoit Cloitre, Oct 06 2004

Cf. A076788, A099217, A099218, A099219, A099220, A099221, A099223, A099224.

RealDigits[ N[ PolyLog[8, 1/2], 105]][[1]] (* Jean-François Alcover, Nov 07 2012 *)

polylog(8,1/2) \\ Charles R Greathouse IV, Jul 14 2014

Li_8(1/2)=sum(k>0, 1/2^k/k^8)=0.500996659...

A099223 Decimal expansion of Li_9(1/2).

Original entry on oeis.org

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

Offset: 0

Benoit Cloitre, Oct 06 2004

Cf. A076788, A099217, A099218, A099219, A099220, A099221, A099222, A099224.

RealDigits[ N[ PolyLog[9, 1/2], 105]][[1]] (* Jean-François Alcover, Nov 07 2012 *)

polylog(9,1/2) \\ Charles R Greathouse IV, Jul 14 2014

Li_9(1/2)=sum(k>0, 1/2^k/k^9)=0.5004948881...

A099224 Decimal expansion of Li_{10}(1/2).

Original entry on oeis.org

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

Offset: 0

Benoit Cloitre, Oct 06 2004

Cf. A076788, A099217, A099218, A099219, A099220, A099221, A099222, A099223.

RealDigits[ N[ PolyLog[10, 1/2], 105]][[1]] (* Jean-François Alcover, Nov 07 2012 *)

polylog(10,1/2) \\ Charles R Greathouse IV, Jul 14 2014

Li_{10}(1/2)=sum(k>0, 1/2^k/k^10)=0.500246320606006775...

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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A099218 Decimal expansion of Li_4(1/2).

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A099219 Decimal expansion of Li_5(1/2).

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A099220 Decimal expansion of Li_6(1/2).

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A099221 Decimal expansion of Li_7(1/2).

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A099222 Decimal expansion of Li_8(1/2).

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A099223 Decimal expansion of Li_9(1/2).

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A099224 Decimal expansion of Li_{10}(1/2).

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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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