loglog การใช้

• It appears first in Flajolet / Martin ( 1985 ) " Probabitistic Counting Algorithms for Data Base Applications " and is further refined by Durand / Flajolet ( 2003 ) in " Loglog Counting of Large Cardinalities ".
• Later it has been refined in " LogLog counting of large cardinalities " by Marianne Durand and Philippe Flajolet, and " HyperLogLog : The analysis of a near-optimal cardinality estimation algorithm " by Philippe Flajolet et al.
• So far, I have tried, separately : ( 1 ) Euler-Maclauren summation, ( 2 ) expressing the summand using Vieta's formula ( 3 ) writing the sine factor as an exponential and looking for telescoping terms in the series, and ( 4 ) trying to relate the sum to an entire function whose order necessarily contains a loglog term ( see [ http : / / en . wikipedia . org / wiki / Entire _ function ).