On a conjecture by Karlin and Szego

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In 1961, Karlin and Szego conjectured : If {P-n(x)}(infinity)(n=0) is an orthogonal polynomial system and {P'(n)(x)}(infinity)(n=1) is a Sturm sequence, then {P-n(x)}(infinity)(n=0) essentially (that is, after a linear change of variable) a classical orthogonal polynomial system of Jacobi, Laguerre, or Hermite. Here,we prove that for any orthogonal polynomial system {P-n(x)}(infinity)(n=0), {P'(n)(x)}(infinity)(n=1) is always a Sturm sequence. Thus, in particular, the above conjecture by Karlin and Szego is false.
Publisher
AMER MATHEMATICAL SOC
Issue Date
1996-01
Language
English
Article Type
Article
Citation

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, v.124, no.1, pp.227 - 231

ISSN
0002-9939
URI
http://hdl.handle.net/10203/75720
Appears in Collection
MA-Journal Papers(저널논문)
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