A099221 -id:A099221 - 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

A099217 Decimal expansion of Li_3(1/2).

Original entry on oeis.org

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

Offset: 0

Benoit Cloitre, Oct 06 2004

			0.537213193608040200940623225594965826670402499340...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.3, p. 44.
L. Lewin, Polylogarithms and associated Functions, North Holland (1981) A.2.6(3)

R. Barbieri, J. A. Mignaco, and E. Remiddi, Electron form factors up to fourth order. I, Il Nuovo Cim. 11A (4) (1972) 824-864, variable a_3 and table II (15).
Michael I. Shamos, A catalog of the real numbers, (2007). See p. 473.

Cf. A076788, A099218, A099219, A099220, A099221, A099222, A099223, A099224.

RealDigits[PolyLog[3, 1/2], 10, 104] // First (* Jean-François Alcover, Feb 13 2013 *)

polylog(3,1/2) \\ Charles R Greathouse IV, Jul 14 2014

Li_3(1/2) = Sum_{k>0} 1/(2^k*k^3) = 0.537213193608...

Li_3(1/2) = 7*zeta(3)/8-Pi^2*log(2)/12+log(2)^3/6. - Benoit Cloitre, May 22 2006

Leading zero removed 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...

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...

cp's OEIS Frontend

A099218 Decimal expansion of Li_4(1/2).

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A099217 Decimal expansion of Li_3(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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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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