A000134 Positive zeros of Bessel function of order 0 rounded to nearest integer. (Formerly M1570 N0613)

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

David W. Wilson, Table of n, a(n) for n = 1..1000

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].

Index entries for sequences related to Bessel functions or polynomials

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

Adjacent sequences: A000131 A000132 A000133 * A000135 A000136 A000137

Keyword

nonn

Author

N. J. A. Sloane

Status

approved