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A245058 Decimal expansion of the real part of Li_2(I), negated. 1
2, 0, 5, 6, 1, 6, 7, 5, 8, 3, 5, 6, 0, 2, 8, 3, 0, 4, 5, 5, 9, 0, 5, 1, 8, 9, 5, 8, 3, 0, 7, 5, 3, 1, 4, 8, 6, 5, 2, 3, 6, 8, 7, 3, 7, 6, 5, 0, 8, 4, 9, 8, 0, 4, 7, 1, 6, 9, 4, 4, 7, 7, 8, 6, 7, 1, 2, 5, 0, 9, 3, 3, 8, 0, 0, 4, 0, 0, 1, 0, 9, 2, 2, 9, 2, 0, 3, 6, 1, 2, 5, 7, 7, 4, 6, 9, 8, 3, 8, 1, 6, 3, 0, 0, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This is the decimal expansion of the real part of the dilogarithm of the square root of -1. The imaginary part is Catalan's number (A006752).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000 (terms 0..104 from Robert G. Wilson v)

FORMULA

Also equals -zeta(2)/8 = -Pi^2/48.

Also equals the Bessel moment Integral_{0..inf} x I_1(x) K_0(x)^2 K_1(x) dx. - Jean-Fran├žois Alcover, Jun 05 2016

From Terry D. Grant, Sep 11 2016: (Start)

Equals Sum_{n>=1} (-1)^n/(2n+2)^2.

Equals (Sum_{n>=1} 1/(2n)^2)/2 = A222171/2. (End)

EXAMPLE

0.2056167583560283045590518958307531486523687376508498047169447786712509338004...

MATHEMATICA

RealDigits[ Re[ PolyLog[2, I]], 10, 111][[1]] (* or *) RealDigits[ Zeta[2]/8, 10, 111][[1]] (* or *) RealDigits[ Pi^2/48, 10, 111][[1]]

PROG

(PARI) zeta(2)/8 \\ Charles R Greathouse IV, Aug 27 2014

(Sage)

evenalt = (i for i in NN if i>1 and is_even(i))

s = RLF(0); s

RealField(110)(s)

for i in xrange(0, 50000000): s += ((-1)^(i+1)) / ((evenalt.next())^2)

print s # Terry D. Grant, Sep 11 2016

(MAGMA) SetDefaultRealField(RealField(100)); R:=RealField(); Pi(R)^2/48; // G. C. Greubel, Aug 25 2018

CROSSREFS

Cf. A006752, A072691, A222171, A242301.

Sequence in context: A155524 A051111 A068558 * A240657 A262420 A240662

Adjacent sequences:  A245055 A245056 A245057 * A245059 A245060 A245061

KEYWORD

nonn,cons

AUTHOR

Robert G. Wilson v, Aug 21 2014

STATUS

approved

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Last modified September 15 16:12 EDT 2019. Contains 327078 sequences. (Running on oeis4.)