Monotonicity of zeros of Laguerre polynomials
نویسندگان
چکیده
منابع مشابه
Monotonicity of zeros of Laguerre–Sobolev-type orthogonal polynomials
Article history: Received 15 December 2008 Available online 3 March 2010 Submitted by D. Waterman
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Denote by xn,k(α, β), k = 1, . . . , n, the zeros of the Jacobi polynomial P (α,β) n (x). It is well known that xn,k(α, β) are increasing functions of β and decreasing functions of α. In this paper we investigate the question of how fast the functions 1 − xn,k(α, β) decrease as β increases. We prove that the products tn,k(α, β) := fn(α, β) (1− xn,k(α, β)), where fn(α, β) = 2n2 + 2n(α + β + 1) +...
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Monotonicity of zeros of orthogonal Laurent polynomials associated with a strong distribution with respect to a parameter is discussed. A natural analog of a classical result of A. Markov is proved. Recent results of Ismail and Muldoon based on the Hellman-Feynman theorem are also extended to a monotonicity criterion for zeros of Laurent polynomials. Results concerning the behaviour of extreme ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2009
ISSN: 0377-0427
DOI: 10.1016/j.cam.2009.02.038