A276709 - OEIS

A276709

Decimal expansion of the derivative of logarithmic integral at its positive real root.

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

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OFFSET

1,1

COMMENTS

Since the real root location of li(x) is the Soldner's constant A070769, this constant equals 1/log(A070769). It is also the inverse of the unique real root A091723 of the exponential integral function Ei(x).

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 1/log(A070769) and 1/A091723.

EXAMPLE

2.68451035082070765250238264048723868531017973459855163522041486450...

MATHEMATICA

1/x/.FindRoot[ExpIntegralEi[x] == 0, {x, 1}, WorkingPrecision -> 104] (* Vaclav Kotesovec, Sep 27 2016 *)

PROG

(PARI) li(z) = {my(c=z+0.0*I); \\ Computes li(z) for any complex z