Monotonicity Properties of the Zeros of Ultraspherical Polynomials
作者: Árpád ElbertPanayiotis D. Siafarikas
作者单位: 1Mathematical Institute of the Hungarian Academy of Sciences, Reáltanoda u. 13-15, H-1053, Budapest, Hungary
2Department of Mathematics, University of Patras, Patras, Greece
刊名: Journal of Approximation Theory, 1999, Vol.97 (1), pp.31-39
来源数据库: Elsevier Journal
DOI: 10.1006/jath.1996.3259
原始语种摘要: Abstract(#br)Let x ( λ ) n , k , k =1,2,…,[ n /2], denote the k th positive zero in increasing order of the ultraspherical polynomial P ( λ ) n ( x ). We prove that the function [ λ +(2 n 2 +1)/(4 n +2)] 1/2 x ( λ ) n , k increases as λ increases for λ >−1/2. The proof is based on two integrals involved with the square of the ultraspherical polynomial P ( λ ) n ( x ).
全文获取路径: Elsevier  (合作)
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影响因子:0.755 (2012)

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关键词翻译
关键词翻译
  • polynomial 多项式
  • prove 实验
  • increasing 增加的
  • proof 证明
  • denote 指示
  • square 正方形
  • function 函数
  • involved 涉及
  • based 基于
  • positive 阳片