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A340782
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).
0
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, 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, 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
OFFSET
0,1
REFERENCES
Francois Le Lionnais, Les nombres remarquables, Paris, Hermann, 1983, p. 25.
EXAMPLE
-0.3847901973793791729759092256322942220633230399509112463798587588...
MATHEMATICA
digits = 105;
x[n_Integer] := x[n] = BesselJZero[1, n];
f[n_Integer] := f[n] = 1/(x[n] BesselJ[0, x[n]]);
NSum[f[n], {n, 1, Infinity}, Method -> "AlternatingSigns", WorkingPrecision -> digits+10] // RealDigits[#, 10, digits][[1]]&
CROSSREFS
Sequence in context: A276682 A303215 A240242 * A010628 A225456 A366271
KEYWORD
nonn,cons
AUTHOR
STATUS
approved