OFFSET
1,1
LINKS
Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 16.
Kevin Ford, The distribution of Totients
FORMULA
Let F(x) = sum_{k >= 1} ((k+1)*log(k+1) - k*log(k) - 1)*x^k.
C = 1/(2*|log(rho)|), where rho is the unique solution on [0,1) of F(rho)=1.
D = 2*C*(1 + log(F'(rho)) - log(2*C)) - 3/2.
EXAMPLE
2.176968743559410321739727298735814329767273758965844960238628...
MATHEMATICA
digits = 99; F[x_?NumericQ] := NSum[((k + 1)*Log[k + 1] - k*Log[k] - 1)*x^k, {k, 1, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 1000]; F'[x_?NumericQ] := NSum[((k + 1)*Log[k + 1] - k*Log[k] - 1)*k*x^(k - 1), {k, 1, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 1000]; rho = x /. FindRoot[F[x] == 1, {x, 5/10, 6/10}, WorkingPrecision -> digits + 10]; c = -1/(2*Log[rho]); d = 2*c*(1 + Log[F'[rho]] - Log[2*c]) - 3/2; RealDigits[d, 10, digits] // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Sep 02 2014
STATUS
approved