# An interpolation-theoretical characterization of the classical orthogonal polynomials

An interpolation-theoretical characterization of the classical orthogonal polynomials Acta Mathematica Academiae Seientiarum IIungaricae Tomus 26 (1--2), (1975), 163--169. AN INTERPOLATION-THEORETICAL CHARACTERIZATION OF THE CLASSICAL ORTHOGONAL POLYNOMIALS By I. JO0 (Budapest) 1. The Jacobi, the Laguerre and the Hermite polynomials together form the so called "classical" orthogonal polynomials (in the strict sense of'the word). They are characterized by their several particular properties (see ACZs , FELDMaNN , MIKOLAS , LESKY , HAHN , KRALL , CSASZ~R ). An interpolation theoretical characterization was given by EG]~RVARY and TURIN , [9J for the Legendre and Hermite polynomials, further for the Laguerre polynomials with the parameter 0. BALAZS [1(3] characterized the ultraspherical polynomials and Jo6  characterized the Laguerre polynomials with the parameter 1 in a similar way. The method appeared first in  seems very useful on several parts of the approxi- mation theory (see for example FRZUD  Theorem (IIL1.6)). In the present paper we shall give an interpolation-theoretical characterization for all Jacobi and Laguerre polynomials. Adding these results to the results of ,  we obtain a complete interpolation-theoretical chalacterization of all classical orthogonal polynomials. 2. Let (1) a< :q < x2 <... < x,,< b be n points in (a, b) and let the fundamental interpolation polynomials http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Academiae Scientiarum Hungarica Springer Journals

# An interpolation-theoretical characterization of the classical orthogonal polynomials

, Volume 26 (2) – May 21, 2016
7 pages      /lp/springer-journals/an-interpolation-theoretical-characterization-of-the-classical-B0p1ZVDZDP
Publisher
Springer Journals
Subject
Mathematics; Mathematics, general
ISSN
0001-5954
eISSN
1588-2632
DOI
10.1007/BF01895959
Publisher site
See Article on Publisher Site

### Abstract

Acta Mathematica Academiae Seientiarum IIungaricae Tomus 26 (1--2), (1975), 163--169. AN INTERPOLATION-THEORETICAL CHARACTERIZATION OF THE CLASSICAL ORTHOGONAL POLYNOMIALS By I. JO0 (Budapest) 1. The Jacobi, the Laguerre and the Hermite polynomials together form the so called "classical" orthogonal polynomials (in the strict sense of'the word). They are characterized by their several particular properties (see ACZs , FELDMaNN , MIKOLAS , LESKY , HAHN , KRALL , CSASZ~R ). An interpolation theoretical characterization was given by EG]~RVARY and TURIN , [9J for the Legendre and Hermite polynomials, further for the Laguerre polynomials with the parameter 0. BALAZS [1(3] characterized the ultraspherical polynomials and Jo6  characterized the Laguerre polynomials with the parameter 1 in a similar way. The method appeared first in  seems very useful on several parts of the approxi- mation theory (see for example FRZUD  Theorem (IIL1.6)). In the present paper we shall give an interpolation-theoretical characterization for all Jacobi and Laguerre polynomials. Adding these results to the results of ,  we obtain a complete interpolation-theoretical chalacterization of all classical orthogonal polynomials. 2. Let (1) a< :q < x2 <... < x,,< b be n points in (a, b) and let the fundamental interpolation polynomials

### Journal

Acta Mathematica Academiae Scientiarum HungaricaSpringer Journals

Published: May 21, 2016

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