- #1
cameronm
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The logarithmic integral function, which is what you get by integrating 1/ln(x), is closely linked to prime numbers. It approximates the number of primes smaller than x. Heres an infinite series which describes the function:
[tex]li(x)=\gamma+ln(ln(x))+\sum^{\infty}_{n=1}\frac{ln(x)^n}{n*n!}[/tex]
where [tex]\gamma[/tex] is the Euler–Mascheroni constant.
This infinite series is a continuous function and maps x to li(x) on a 1-to-1 basis.
Therefore, in theory there should be an inverse function of li, right? But I'm having difficulty finding it.
Thanks for any help guys :)
[tex]li(x)=\gamma+ln(ln(x))+\sum^{\infty}_{n=1}\frac{ln(x)^n}{n*n!}[/tex]
where [tex]\gamma[/tex] is the Euler–Mascheroni constant.
This infinite series is a continuous function and maps x to li(x) on a 1-to-1 basis.
Therefore, in theory there should be an inverse function of li, right? But I'm having difficulty finding it.
Thanks for any help guys :)