

A257819


Decimal expansion of the real part of li(1).


3



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

1,1


COMMENTS

The logarithmic integral function li(z) has a cut along the negative real axis which causes therein a discontinuity in the imaginary part of li(z). The real part of li(z), however, is well behaved for any real z, except the singularity at z=+1. At z=1, real(li(z)) attains its absolute maximum, and also its only local maximum, on the real interval (infinity,+1). The corresponding imaginary part is described in A257820.


LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..2000
Eric Weisstein's World of Mathematics, Logarithmic Integral
Wikipedia, Logarithmic integral function


FORMULA

Equals gamma+log(Pi)+Sum[k=1..infinity]((1)^k*Pi^(2*k)/(2*k)!/(2*k)).


EXAMPLE

0.073667912046425485990100965230149671869877462328618050265955...


MAPLE

evalf(Re(Li(1)), 120); # Vaclav Kotesovec, May 11 2015


MATHEMATICA

RealDigits[Re[LogIntegral[1]], 10, 120][[1]] (* Vaclav Kotesovec, May 11 2015 *)


PROG

(PARI) li(z) = {my(c=z+0.0*I); \\ If z is real, convert it to complex
if(imag(c)<0, return(Pi*Ieint1(log(c))),
return(+Pi*Ieint1(log(c)))); }
a=real(li(1))


CROSSREFS

Cf. A000796, A001620, A053510, A257817, A257818, A257820, A257821.
Sequence in context: A019819 A215693 A197028 * A182111 A023643 A050009
Adjacent sequences: A257816 A257817 A257818 * A257820 A257821 A257822


KEYWORD

nonn,cons


AUTHOR

Stanislav Sykora, May 11 2015


STATUS

approved



