Multiple orthogonal polynomials, 𝑑-orthogonal polynomials, production matrices, and branched continued fractions
Copyright policy )Multiple orthogonal polynomials, 𝑑-orthogonal polynomials, production matrices, and branched continued fractions
I analyze an unexpected connection between multiple orthogonal polynomials, d d -orthogonal polynomials, production matrices and branched continued fractions. This work can be viewed as a partial extension of Viennot’s combinatorial theory of orthogonal polynomials to the case where the production matrix is lower-Hessenberg but is not necessarily tridiagonal.
- New York University United States
- University College London United Kingdom
\(d\)-orthogonal polynomial, Exact enumeration problems, generating functions, Matrix equations and identities, Basic linear algebra, Special matrices, multiple orthogonal polynomial, Moment problems and interpolation problems in the complex plane, Łukasiewicz path, production matrix, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), lower-Hessenberg matrix, Mathematics - Classical Analysis and ODEs, branched continued fraction, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics - Combinatorics, 42C05 (Primary), 05A15, 05A19, 15A24, 15A99, 15B99, 30B70, 30E05, 33C45, 41A21 (Secondary), Combinatorics (math.CO), Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Padé approximation, Combinatorial identities, bijective combinatorics, Continued fractions; complex-analytic aspects
\(d\)-orthogonal polynomial, Exact enumeration problems, generating functions, Matrix equations and identities, Basic linear algebra, Special matrices, multiple orthogonal polynomial, Moment problems and interpolation problems in the complex plane, Łukasiewicz path, production matrix, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), lower-Hessenberg matrix, Mathematics - Classical Analysis and ODEs, branched continued fraction, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics - Combinatorics, 42C05 (Primary), 05A15, 05A19, 15A24, 15A99, 15B99, 30B70, 30E05, 33C45, 41A21 (Secondary), Combinatorics (math.CO), Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Padé approximation, Combinatorial identities, bijective combinatorics, Continued fractions; complex-analytic aspects
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