Interlacing of the zeros of Jacobi polynomials with different parameters

DOI10.1007/s11075-008-9162-2zbMath1169.30002OpenAlexW1986495266MaRDI QIDQ1014751

Kerstin Jordaan, Norbert Mbuyi, Kathy A. Driver

Publication date: 29 April 2009

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-008-9162-2

zbMATH Keywords

Jacobi polynomialsseparation resultszeros of Jacobi polynomialscontiguous hypergeometric polynomialsinterlacing properties of zeros

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) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15)

Related Items

Interlacing properties and bounds for zeros of \({}_2\phi_1\) hypergeometric and little \(q\)-Jacobi polynomials, Zeros of Jacobi polynomials \(P_{n}^{(\alpha ,\beta)} \), \(- 2 < \alpha\), \(\beta < -1\), Zeros of quasi-orthogonal Jacobi polynomials, Mixed recurrence equations and interlacing properties for zeros of sequences of classical \(q\)-orthogonal polynomials, Applications of the monotonicity of extremal zeros of orthogonal polynomials in interlacing and optimization problems, Stieltjes interlacing of zeros of little \(q\)-Jacobi and \(q\)-Laguerre polynomials from different sequences, Zeros of Jacobi and ultraspherical polynomials, Interlacing and bounds of zeros of quasi-orthogonal little \(q\)-Jacobi polynomials, Rational Krylov methods for functions of matrices with applications to fractional partial differential equations, Inequalities for zeros of Jacobi polynomials via Obrechkoff’s theorem, Zeros of Orthogonal Polynomials, Interlacing of zeros of Laguerre polynomials of equal and consecutive degree, Uniform Error Estimates for the Lanczos Method, Mixed recurrence relations and interlacing of the zeros of some \(q\)-orthogonal polynomials from different sequences, Monotonicity of zeros of polynomials orthogonal with respect to an even weight function, Gaussian, Lobatto and Radau positive quadrature rules with a prescribed abscissa, Interlacing of zeros of linear combinations of classical orthogonal polynomials from different sequences, Quasi orthogonal Jacobi polynomials and best one-sided \(L_1\) approximation to step functions, Interlacing of zeros of orthogonal polynomials under modification of the measure, Interlacing theorems for the zeros of some orthogonal polynomials from different sequences, Properties of Clifford-Legendre polynomials, Common and interlacing zeros of families of Laguerre~polynomials

Uses Software

• SPECFUN

Cites Work

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• On the behaviour of zeros of Jacobi polynomials
• Separation theorems for the zeros of certain hypergeometric polynomials
• Contiguous relations of hypergeometric series
• Interlacing properties of the zeros of the orthogonal polynomials and approximation of the Hilbert transform
• Gröbner basis and the problem of contiguous relations
• Linear Combinations of Orthogonal Polynomials Generating Positive Quadrature Formulas
• New Inequalities for the Zeros of Jacobi Polynomials