Block orthogonal polynomials: II. Hermite and Laguerre standard block orthogonal polynomials

DOI10.1088/1751-8113/40/10/010zbMATH Open1112.33008arXivmath-ph/0606038OpenAlexW2094356700MaRDI QIDQ3427270

J.-M. Normand

Publication date: 16 March 2007

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Abstract: The standard block orthogonal (SBO) polynomials $P_{i;n}(x),0leilen$ are real polynomials of degree $n$ which are orthogonal with respect to a first Euclidean scalar product to polynomials of degree less than $i$. In addition, they are mutually orthogonal with respect to a second Euclidean scalar product. Applying the general results obtained in a previous paper, we determine and investigate these polynomials when the first scalar product corresponds to Hermite (resp. Laguerre) polynomials. These new sets of polynomials, we call Hermite (resp. Laguerre) SBO polynomials, provide a basis of functional spaces well-suited for some applications requiring to take into account special linear constraints which can be recast into an Euclidean orthogonality relation.

Full work available at URL: https://arxiv.org/abs/math-ph/0606038

zbMATH Keywords

orthogonal polynomialsHermite polynomialsLaguerre polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Many-body theory; quantum Hall effect (81V70) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Applications of hypergeometric functions (33C90)

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