A characterization of Hermite polynomials

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We show that for any orthogonal polynomials {R(n)(x)}(infinity)(n=0) satisfying a spectral type differential equation of order N (greater than or equal to 2) L(N)[y](x) = (i=1)Sigma(N) l(i)(x)y((i))(x) = lambda(n)y(x), {P-n(x)}(infinity)(n=0) must be essentially Hermite polynomials if and only if the leading coefficient l(N)(x) is a nonzero constant.
Publisher
ELSEVIER SCIENCE BV
Issue Date
1997-02
Language
English
Article Type
Article
Keywords

ORTHOGONAL POLYNOMIALS; DIFFERENTIAL-EQUATIONS

Citation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, v.78, no.2, pp.295 - 299

ISSN
0377-0427
URI
http://hdl.handle.net/10203/68112
Appears in Collection
MA-Journal Papers(저널논문)
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