Logarithmic integral function: Difference between revisions

Revision as of 07:22, 20 November 2002

Revision as of 19:29, 20 November 2002

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:π(''x'') ~ Li(''x'')

where π(''x'') denotes the number of primes smaller than or equal to ''x'', and Li(''x'') is the [[offset logarithmic integral]] function. This is, related to theli(''x'') logarithmic integral described above sinceby Li(''x'') = li(''x'') - li(2). ItThe offset logarithmic integral gives a slightly better estimate to the π function than li(''x'').

The function li(''x'') is related to the ''[[exponential integral]]'' Ei(''x'') via the equation