OFFSET
1,1
COMMENTS
This constant is quite close to 5*Pi/2 - 1/8 = 7.72898...
Searching for solutions x=k*Pi+Pi/2-e and small e, for k=1,2,3.... means via the approximation tan(x) = 1/e-e/3-e^3/45... that e is approximately 1/(k*Pi+Pi/2), so the constants x are close to k*Pi+Pi/2-1/(k*Pi+Pi/2). Here k=2 and the constant is close to 5*Pi/2-2/(5*Pi) = 7.7266576... - R. J. Mathar, Jul 11 2024
LINKS
Eric Weisstein's World of Mathematics, du Bois-Reymond Constants.
EXAMPLE
7.72525183693770716419506893306298662637815930461...
MATHEMATICA
xi[n_] := x /. FindRoot[Tan[x] == x, {x, n*Pi + Pi/2 - 1/(4*n)}, WorkingPrecision -> 102]; RealDigits[xi[2]] // First
PROG
(PARI) solve(x=7, 7.8, tan(x)-x) \\ Charles R Greathouse IV, Apr 20 2016
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Feb 20 2015
STATUS
approved