Revision as of 22:59, 6 February 2005 edit Gene Ward Smith (talk \| contribs) Extended confirmed users 3,261 edits offset logarithmic integral ← Previous edit		Revision as of 00:00, 7 February 2005 edit undo Gene Ward Smith (talk \| contribs) Extended confirmed users 3,261 edits The claims that li is mainly used in number theory and that Li gives a better estimate are incorrect and were removed Next edit →
Line 16: (see [[big O notation]]). The logarithmic integral isfinds ~~mainly~~application ~~important~~in ~~because~~many areas, in particular it ~~occurs~~is used is in estimates of [[prime number]] densities, ~~especially~~such inas the [[prime number theorem]]: :π(''x'') ~ li(''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, related to li(''x'') by Li(''x'') = li(''x'') - li(2)~~. ~~The 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 :li(''x'') = Ei (ln (''x''))    for all positive real ''x'' ≠ 1.

Logarithmic integral function: Difference between revisions