A152115 - OEIS

A152115

Decimal expansion of the dilogarithm of (the golden mean minus 1), Li_2(phi-1).

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

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OFFSET

0,1

COMMENTS

Equals Li_2(phic) = L(phic)-log(phic)*log(1-phic)/2 = A002388/10 - A002390^2, where Li_2(.) is the dilogarithm, L(.) is Roger's dilogarithm, where phic = phi-1 = A094214, where -log(phic)= A002390 = log(1-phic)/2.

REFERENCES

L. B. W. Jolley, Summation of Series, Dover (1961)

LINKS

Table of n, a(n) for n=0..104.

Anatol N. Kirillov, Dilogarithm identities, arXiv:hep-th/9408113.

J. H. Loxton, Special values of the dilogarithm function, Acta Arithm. 43 (2) (1984), 155-166.

FORMULA

Equals sum_{n>=1} x^n/n^2 for x= 2*sin(Pi/10). [Jolley eq (360d)]

EXAMPLE

Equals 0.7553956195317414693865200287560823535149635906747...

MATHEMATICA

RealDigits[ PolyLog[2, (Sqrt[5]-1)/2], 10, 105] // First (* Jean-François Alcover, Feb 12 2013 *)

PROG

(PARI) phic=(sqrt(5)-1)/2 ; dilog(phic);

CROSSREFS

Sequence in context: A295219 A138313 A138312 * A098842 A173166 A070273

Adjacent sequences: A152112 A152113 A152114 * A152116 A152117 A152118

KEYWORD

cons,easy,nonn

AUTHOR

R. J. Mathar, Nov 24 2008

EXTENSIONS

More terms from Jean-François Alcover, Feb 12 2013

STATUS

approved