TY - JOUR
T1 - Equioscillatory property of the Laguerre polynomials
AU - Krasikov, Ilia
AU - Zarkh, Alexander
N1 - Funding Information:
The work of second author was supported by the EC Marie Curie programme NET-ACE ( MEST-CT-2004-6724 ).
PY - 2010/11
Y1 - 2010/11
N2 - We show that the function ((x-dm)(x-dM))1/4xα/2e-x/2Lk(α)(x) is almost equioscillating with the amplitude 2/π provided k and α are large enough. Here Lk(α)(x) is the orthonormal Laguerre polynomial of degree k and dm, dM are some approximations for the extreme zeros. As a corollary we obtain a very explicit, uniform in k and α, sharp upper bound on the Laguerre polynomials.
AB - We show that the function ((x-dm)(x-dM))1/4xα/2e-x/2Lk(α)(x) is almost equioscillating with the amplitude 2/π provided k and α are large enough. Here Lk(α)(x) is the orthonormal Laguerre polynomial of degree k and dm, dM are some approximations for the extreme zeros. As a corollary we obtain a very explicit, uniform in k and α, sharp upper bound on the Laguerre polynomials.
KW - Bounds
KW - Inequalities
KW - Laguerre polynomials
KW - Orthogonal polynomials
UR - http://www.scopus.com/inward/record.url?scp=78049378853&partnerID=8YFLogxK
U2 - 10.1016/j.jat.2010.06.004
DO - 10.1016/j.jat.2010.06.004
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AN - SCOPUS:78049378853
SN - 0021-9045
VL - 162
SP - 2021
EP - 2047
JO - Journal of Approximation Theory
JF - Journal of Approximation Theory
IS - 11
ER -