%I #17 Jan 22 2021 09:16:40

%S 3,8,4,7,9,0,1,9,7,3,7,9,3,7,9,1,7,2,9,7,5,9,0,9,2,2,5,6,3,2,2,9,4,2,

%T 2,2,0,6,3,3,2,3,0,3,9,9,5,0,9,1,1,2,4,6,3,7,9,8,5,8,7,5,8,8,0,0,2,7,

%U 0,9,0,5,5,0,3,6,2,0,0,5,7,6,5,1,3,0,0,9,5,8,3,9,4,0,1,4,5,8,4,6,6,1,0,4,5

%N Decimal expansion of Sum_{n>=1} 1/(x(n)*J0(x(n))) where x(n) is the n-th zero of Bessel's function J1(x) (negated).

%D Francois Le Lionnais, Les nombres remarquables, Paris, Hermann, 1983, p. 25.

%e -0.3847901973793791729759092256322942220633230399509112463798587588...

%t digits = 105;

%t x[n_Integer] := x[n] = BesselJZero[1, n];

%t f[n_Integer] := f[n] = 1/(x[n] BesselJ[0, x[n]]);

%t NSum[f[n], {n, 1, Infinity}, Method -> "AlternatingSigns", WorkingPrecision -> digits+10] // RealDigits[#, 10, digits][[1]]&

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Jan 21 2021