Characterizations of Classical Orthogonal Polynomials
Copyright policy )Characterizations of Classical Orthogonal Polynomials
In the literature several characterization theorems for the so-called classical orthogonal polynomials are known [cf. \textit{S. Bochner}, Math. Z. 29, 730-736 (1929), \textit{W. Hahn}, Math. Z. 39, 634-638 (1935), \textit{W. A. Al-Salam}, Orthogonal polynomials: theory and practice, Proc. NATO ASI, Colombus/OH (USA) 1989, NATO ASI Ser., Ser. C 294, 1-24 (1990; Zbl 0704.42021) and references in the last mentioned paper]. The authors give a simple unified proof of (the equivalence) of these characterizations and finally state one of the results in such a way that generalization to orthogonal polynomial sequences satisfying higher order differential equations is relatively simple.
- Korea Advanced Institute of Science and Technology Korea (Republic of)
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, classical orthogonal polynomials
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, classical orthogonal polynomials
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