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

Offset: 1

Author

Stanislav Sykora, Sep 15 2016

Keywords

• nonn
• cons

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).

Examples

			2.68451035082070765250238264048723868531017973459855163522041486450...
		

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. A070769, A091723, A257821.

Programs

Mathematica

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

PARI

li(z) = {my(c=z+0.0*I); \\ Computes li(z) for any complex z
if(imag(c)<0,return(-Pi*I-eint1(-log(c))),return(+Pi*I-eint1(-log(c))));}
a = 1/log(solve(x=1.1,2.0,real(li(x)))) \\ Computes this constant

Formula

Equals 1/log(A070769) and 1/A091723.