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A172263
a(n) is the greatest zero of Hermite polynomial H(n,x) to nearest integer
0
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
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
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jan 30 2010
STATUS
approved