

A257820


Decimal expansion of the absolute value of the imaginary part of li(1).


3



3, 4, 2, 2, 7, 3, 3, 3, 7, 8, 7, 7, 7, 3, 6, 2, 7, 8, 9, 5, 9, 2, 3, 7, 5, 0, 6, 1, 7, 9, 7, 7, 4, 2, 8, 0, 5, 4, 4, 4, 3, 9, 4, 4, 2, 8, 6, 6, 8, 7, 0, 7, 8, 2, 0, 2, 9, 2, 2, 5, 6, 0, 7, 8, 0, 3, 0, 8, 9, 0, 0, 9, 3, 3, 0, 9, 4, 5, 2, 8, 5, 7, 8, 4, 6, 7, 2, 7, 7, 4, 9, 1, 7, 4, 0, 1, 3, 2, 9, 1, 6, 9, 2, 7, 5
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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). However, the absolute value of the imaginary part is continuous and its value is a well behaved function of any real argument, excepting z=+1. The above value corresponds to imag(li(z)) at z=1, the point where the corresponding real part (A257819) attains its maximum within the real interval (infinity,+1).


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 Pi*(1/2 + Sum[k=0..infinity]((1)^k*Pi^(2*k)/(2*k+1)!/(2*k+1))).


EXAMPLE

3.422733378777362789592375061797742805444394428668707820292256...


MAPLE

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


MATHEMATICA

RealDigits[Im[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=imag(li(1))


CROSSREFS

Cf. A000796, A257817, A257818, A257819, A257822.
Sequence in context: A205786 A213812 A143486 * A159273 A021749 A254175
Adjacent sequences: A257817 A257818 A257819 * A257821 A257822 A257823


KEYWORD

nonn,cons


AUTHOR

Stanislav Sykora, May 11 2015


STATUS

approved



