In mathematics, the logarithmic integral function or integral logarithm li (x) is a special function. It is relevant in problems of physics and has number theoretic significance.

Apr 12, 2025 · The logarithmic integral (in the "American" convention; Abramowitz and Stegun 1972; Edwards 2001, p. 26), is defined for real x as li (x) = {int_0^x (dt)/ (lnt) for 0<x<1; …

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The logarithmic integral function Li(x) (or just the “logarithmic integral”) is a locally summable function on the real line. This special function is used in physics and number theory, most …

The logarithmic integral can be expressed as an infinite series: li(x) = γ + ln(ln(x)) + Σ ∞ n=1 ln(x) n / (n⋅n!) where γ is the Euler-Mascheroni constant 0.57721566490153286... For large values …

Logarithmic integral function li(x) is a special function for solving certain problems in physics and number theory. It provides a very good approximation to the prime counting function - that …

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Oct 3, 2023 · Here we have the Logarithmic Integral.We integrate from 2 to x for the reciprocal of ln(t). We choose 2 to x as it is key in showing the Prime Number Theorem...

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Jul 25, 2019 · Mathematica suggests that integrating the Logarithamic Integral, li(x) = ∫x0 dt logt, multiplied by xn, between the limits 0 and 1 leads to the following result. ∫1 0xnli(x)dx = − log(n …