Logarithmic integral function: Difference between revisions

Revision as of 19:20, 28 August 2022

Revision as of 11:00, 22 November 2022

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The function li(''x'') has a single positive zero; it occurs at ''x'' ≈ 1.45136 92348 83381 05028 39684 85892 02744 94930... {{OEIS2C|A070769}}; this number is known as the [[Ramanujan–Soldner constant]].

−Li−li(0) = li(2) ≈ 1.045163 780117 492784 844588 889194 613136 522615 578151... {{OEIS2C|A069284}}

This is <math>-(\Gamma\left(0,-\ln 2\right) + i\,\pi)</math> where <math>\Gamma\left(a,x\right)</math> is the [[incomplete gamma function]]. It must be understood as the [[Cauchy principal value]] of the function.