On the zeros of Jacobi polynomials

Elbert, Árpád; Laforgia, Andrea; Rodonò, Lucia G.

doi:10.1007/bf01874695

Cited by 17 publications

(8 citation statements)

References 2 publications

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“…Elbert, Laforgia and Rodonó [10] established lower and upper limits for the zeros of the Jacobi polynomials. In particular, they proved that the inequality…”

Section: Upper Limits For the Positive Zeros Of Gegenbauer And Hermitmentioning

confidence: 99%

Zeros of Gegenbauer and Hermite polynomials and connection coefficients

et al. 2004

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“…Elbert, Laforgia and Rodonó [10] established lower and upper limits for the zeros of the Jacobi polynomials. In particular, they proved that the inequality…”

Section: Upper Limits For the Positive Zeros Of Gegenbauer And Hermitmentioning

confidence: 99%

Zeros of Gegenbauer and Hermite polynomials and connection coefficients

et al. 2004

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“…Sturm's comparison theorem is used in [13] and [14] to obtain inequalities for the zeros of Gegenbauer and Jacobi polynomials respectively and similar classical methods are also described in [46]. Since the zeros of p n are real whenever {p n } ∞ n=0 is an orthogonal sequence, techniques developed to study the properties of zeros of polynomials in the Laguerre-Polya class are useful.…”

Section: Inequalities For the Zerosmentioning

confidence: 99%

Inequalities for Extreme Zeros of Some Classical Orthogonal and q-orthogonal Polynomials

Driver

Jordaan

2013

Math. Model. Nat. Phenom.

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Abstract. Let {pn} ∞ n=0 be a sequence of orthogonal polynomials. We briefly review properties of pn that have been used to derive upper and lower bounds for the largest and smallest zero of pn. Bounds for the extreme zeros of Laguerre, Jacobi and Gegenbauer polynomials that have been obtained using different approaches are numerically compared and new bounds for extreme zeros of q-Laguerre and little q-Jacobi polynomials are proved.

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“…Of special interest are the zeros of the classical families of hypergeometric orthogonal polynomials, which have been fruitfully analyzed e.g. through Sturm-Liouville theory and via Stieltjes' electrostatic interpretation [S75,ALM82,FR86,G87,ELR94,G98,I00,MMM07,JT09,DJ12,ADGR12,ADGP13,S16]. In this work we are mainly concerned with estimates for the locations of the zeros of some well-studied (basic) hypergeometric orthogonal polynomial families belonging to the (q−)Askey scheme [AW85, KLS10], while other relevant issues concerning these zeros, such as e.g.…”

Section: Introductionmentioning

confidence: 99%

Solutions of convex Bethe Ansatz equations and the zeros of (basic) hypergeometric orthogonal polynomials

Diejen

Emsiz

2018

Lett Math Phys

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Via the solutions of systems of algebraic equations of Bethe Ansatz type, we arrive at bounds for the zeros of orthogonal (basic) hypergeometric polynomials belonging to the Askey-Wilson, Wilson and continuous Hahn families. * Whereas a classical result of Bochner characterizes the Jacobi polynomials as "the most general orthogonal family satisfying a linear homogeneous second-order differential equation", the Askey-Wilson polynomials are known to constitute "the most general orthogonal family satisfying a linear homogeneous second-order q-difference equation" [GH96].

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On the zeros of Jacobi polynomials

Cited by 17 publications

References 2 publications

Zeros of Gegenbauer and Hermite polynomials and connection coefficients

Zeros of Gegenbauer and Hermite polynomials and connection coefficients

Inequalities for Extreme Zeros of Some Classical Orthogonal and q-orthogonal Polynomials

Solutions of convex Bethe Ansatz equations and the zeros of (basic) hypergeometric orthogonal polynomials

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