OFFSET
0,1
LINKS
Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 16.
Kevin Ford, The distribution of Totients
FORMULA
Rho is the unique solution on [0,1) of the equation F(rho)=1, where F(x) = sum_{k >= 1} ((k+1)*log(k+1) - k*log(k) - 1)*x^k.
EXAMPLE
0.54259858609847102195938459577946942677950461619539246966515781...
MATHEMATICA
digits = 101; F[x_?NumericQ] := NSum[((k + 1)*Log[k + 1] - k*Log[k] - 1)*x^k, {k, 1, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 1000]; rho = x /. FindRoot[F[x] == 1, {x, 5/10, 6/10}, WorkingPrecision -> digits + 10]; RealDigits[rho, 10, digits] // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Sep 02 2014
STATUS
approved