A257822 Decimal expansion of the absolute value of the imaginary part of li(-A257821).

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

Offset: 1

Author

Stanislav Sykora, May 11 2015

Keywords

• nonn
• cons

Comments

As discussed in A257820, 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=-A257821, the unique point in the real interval (-infinity,+1) where the corresponding real part is zero.

Examples

			3.87450104931287362237096971350633901238405804054504846377340...
		

Links

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

Crossrefs

Cf. A257820, A257821.

Programs

Mathematica

RealDigits[Im[LogIntegral[-a/.FindRoot[Re[LogIntegral[-a]]==0,{a,2},WorkingPrecision->120]]]][[1]] (* Vaclav Kotesovec, May 11 2015 *)

PARI

li(z) = {my(c=z+0.0*I); \\ If z is real, convert it to complex
  if(imag(c)<0, return(-Pi*I-eint1(-log(c))),
  return(+Pi*I-eint1(-log(c)))); }
  root=solve(x=-3,-1,real(li(x)));  \\ Better use excess realprecision
  a=imag(li(root))