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A000134
Positive zeros of Bessel function of order 0 rounded to nearest integer.
(Formerly M1570 N0613)
2
2, 6, 9, 12, 15, 18, 21, 24, 27, 31, 34, 37, 40, 43, 46, 49, 53, 56, 59, 62, 65, 68, 71, 75, 78, 81, 84, 87, 90, 93, 97, 100, 103, 106, 109, 112, 115, 119, 122, 125, 128, 131, 134, 137, 141, 144, 147, 150, 153, 156, 159, 163, 166, 169, 172, 175, 178, 181, 185, 188
OFFSET
1,1
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 409.
British Association Mathematical Tables, Vol. 6, Bessel Functions, Part 1, Functions of Order Zero and Unity. Cambridge Univ. Press, 1937, p. 171.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
FORMULA
a(n) = Pi*n + O(1). Probably a(n+1) - a(n) is 3 or 4 for all n. - Charles R Greathouse IV, Oct 04 2016
MATHEMATICA
Table[BesselJZero[0, n] // Round, {n, 1, 40}] (* Jean-François Alcover, Feb 04 2016 *)
PROG
(PARI) a(n)=if(n<1, 0, n=a(n-1); until(besselj(0, n-1/2)*besselj(0, n+1/2)<0, n++); n)
CROSSREFS
Sequence in context: A287445 A119720 A173978 * A120701 A350235 A189752
KEYWORD
nonn
STATUS
approved