A172263 a(n) is the greatest zero of Hermite polynomial H(n,x) to nearest integer

0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12

Offset

0,5

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. 801.

Links

Table of n, a(n) for n=0..87.

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 Hermite polynomials

Formula

HermiteH(0,x) = 1, HermiteH(1,x) = 2*x,HermiteH(n,x) = 2*x*HermiteH(n-1,x) - 2*(n-1)*HermiteH(n-2,x), for n>1.

Example

H(1,x) = 2x , a(1) = 0 ; H(2,x) = 4*x^2 - 2, a(2) = 1, etc.

Maple

for p from 2 to 1000 do; a:= realroot( expand(HermiteH(p, x)), 1/1000000); print (a); od;

Crossrefs

Sequence in context: A117707 A163352 A087834 * A337635 A140437 A226763

Adjacent sequences: A172260 A172261 A172262 * A172264 A172265 A172266

Keyword

nonn

Author

Michel Lagneau, Jan 30 2010

Status

approved