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// Program to calculate the log integral, often called Li[x]
//
// This is useful in number theory, such as estimating the number of primes
// below a certain number.
//
// See: http://functions.wolfram.com/GammaBetaErf/LogIntegral/06/01/01/0002/
LogIntegral[z] :=
{
lnz = ln[z]
sum = (1/2) (ln[lnz] - ln[1/lnz]) + EulerMascheroniConstant
k = 0
do
{
k = k+1
oldsum = sum
term = lnz^k / (k k!)
sum = sum + term
// println["$k\t$term\t$sum"]
} while (oldsum != sum)
return sum
}
Download or view LogIntegral.frink in plain text format
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Alan Eliasen was born 20136 days, 5 hours, 14 minutes ago.