Interlacing of zeros of linear combinations of classical orthogonal polynomials from different sequences

Driver, Kathy; Jordaan, Kerstin; Mbuyi, Norbert

doi:10.1016/j.apnum.2009.04.007

Cited by 5 publications

(2 citation statements)

References 12 publications

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“…If one of the numerator parameters α 1 , · · · , α p is equal to a negative integer or zero, say α 1 = −n (n ∈ N 0 ), then the series terminates and reduces to a polynomial of degree n in z. The natural question that arises in connection with any polynomials is the correlative properties of its zeros (see, for example, [3,9,11,21]). The hypergeometric polynomials whose properties are best known and understood, including the location of their zeros and their asymptotic zero distribution, are those in the 1 F 1 (Kummer and Whittaker) and 2 F 1 (Gauss) classes (see, for details, [20]), mainly because of their connection with orthogonal polynomials [13].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic distributions of the zeros of certain classes of hypergeometric functions and polynomials

2011

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Abstract. The main object of this paper is to consider the asymptotic distribution of the zeros of certain classes of the Clausenian hypergeometric 3 F 2 functions and polynomials. Some classical analytic methods and techniques are used here to analyze the behavior of the zeros of the Clausenian hypergeometric polynomials:where n is a nonnegative integer. Some families of the hypergeometric 3 F 2 functions, which are connected (by means of a hypergeometric reduction formula) with the Gauss hypergeometric polynomials of the form 2 F 1 (−n, kn + l + 1; kn + l + 2; z), are also investigated. Numerical evidence and graphical illustrations of the clustering of zeros on certain curves are generated by Mathematica (Version 4.0).

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Section: Introductionmentioning

confidence: 99%

Asymptotic distributions of the zeros of certain classes of hypergeometric functions and polynomials

2011

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“…The natural question that arises in connection with any polynomials is the correlative properties of their zeros (see, for example, [5,7,8,9,10,11,21,23,24,27]). For the Gauss hypergeometric polynomials, the Euler integral representation, together with the saddle-point method, would generate the asymptotic zero distribution of some classes of 2 F 1 polynomials [2,3,13,26].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic distributions of the zeros of a family of hypergeometric polynomials

Zhou

Srivástava

Wang

2011

Proc. Amer. Math. Soc.

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Abstract. The main object of this paper is to consider the asymptotic distribution of the zeros of certain classes of the Gauss hypergeometric polynomials. Some classical analytic methods and techniques are used here to analyze the behavior of the zeros of the Gauss hypergeometric polynomials,where n is a nonnegative integer. Owing to the connection between the classical Jacobi polynomials and the Gauss hypergeometric polynomials, we prove a special case of a conjecture made by Martínez-Finkelshtein, Martínez-González and Orive. Numerical evidence and graphical illustrations of the clustering of the zeros on certain curves are generated by Mathematica (Version 4.0).

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Spectral properties related to generalized complementary Romanovski–Routh polynomials

Shukla

Swaminathan

2023

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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Interlacing of zeros of linear combinations of classical orthogonal polynomials from different sequences

Cited by 5 publications

References 12 publications

Asymptotic distributions of the zeros of certain classes of hypergeometric functions and polynomials

Asymptotic distributions of the zeros of certain classes of hypergeometric functions and polynomials

Asymptotic distributions of the zeros of a family of hypergeometric polynomials

Spectral properties related to generalized complementary Romanovski–Routh polynomials

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