Zeros of the Hypergeometric Polynomials F(−n, b; −2n; z)

Driver, Kathy; Möller, Manfred

doi:10.1006/jath.2000.3548

Cited by 30 publications

(26 citation statements)

References 2 publications

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“…However, the figures in [10] actually showed the distribution of the zeros of 2 F 1 (−n, b; −2n; z), not the distribution of the zeros of the function H n (b, u) defined by (5.1).…”

Section: Uniform Distribution Of the Zerosmentioning

confidence: 96%

“…In our paper, the parameters a, b, c, d and τ are independent of the large parameter n. Moreover, the zeros of the Clausenian hypergeometric polynomials: which were investigated in [10], are also distributed uniformly along the unit circle |u| = 1 (see [10,Proposition 4.4]). However, the figures in [10] actually showed the distribution of the zeros of 2 F 1 (−n, b; −2n; z), not the distribution of the zeros of the function H n (b, u) defined by (5.1).…”

Section: Uniform Distribution Of the Zerosmentioning

confidence: 99%

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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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“…However, the figures in [10] actually showed the distribution of the zeros of 2 F 1 (−n, b; −2n; z), not the distribution of the zeros of the function H n (b, u) defined by (5.1).…”

Section: Uniform Distribution Of the Zerosmentioning

confidence: 96%

Section: Uniform Distribution Of the Zerosmentioning

confidence: 99%

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

2011

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“…On the other hand, Driver and Möller [4] proved that, for any real positive b, the zeros of the polynomials…”

Section: Proof Of the Theoremmentioning

confidence: 98%

Asymptotics of zeros of polynomials arising from rational integrals

Dimitrov

2004

Journal of Mathematical Analysis and Applications

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“…Using the Hilbert-Klein formulae [25, Theorem 7.2, p. 145] and the connection between hypergeometric polynomials, 2 F 1 , and the Jacobi polynomials, K. Driver and K. Jordaan [11] recently obtained the following result concerning the zero distribution of hypergeometric polynomials. …”

Section: Distribution Of Zeros Of a Class Of Jacobi Polynomials 4355mentioning

confidence: 99%

The distribution of zeros of a class of Jacobi polynomials

Charalambides

Csordás

2010

Proc. Amer. Math. Soc.

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Abstract. Polynomials whose coefficients are successive derivatives of a class of generalized Laguerre polynomials evaluated at x = 0 are shown to be stable. These polynomials can be expressed in terms of Jacobi polynomials. The authors also prove that a related family of polynomials, depending on a parameter, possess only real and negative zeros. A special class of stability-preserving operators is also investigated.

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Zeros of the Hypergeometric Polynomials F(−n, b; −2n; z)

Cited by 30 publications

References 2 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

Asymptotics of zeros of polynomials arising from rational integrals

The distribution of zeros of a class of Jacobi polynomials

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