A connection between ultraspherical and pseudo-ultraspherical polynomials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:439

Article

Driver, Kathy¹  Muldoon, Martin E.² 

[1] Univ Cape Town, Dept Math & Appl Math, Private Bag X1, ZA-7701 Rondebosch, South Africa

[2] York Univ, Dept Math & Stat, Toronto, ON M3J 1P3, Canada

关键词: Ultraspherical polynomials;    Pseudo-ultraspherical polynomials;    Zeros;    Monotonicity;   

DOI  :  10.1016/j.jmaa.2016.02.050

来源: Elsevier

【 摘 要 】

The pseudo-ultraspherical polynomial of degree n is defined by (C) over tilde ((lambda))(n)(x) = (-i)n C-n((lambda)) (ix) where C-n((lambda)) (x) is the ultraspherical polynomial. We derive a simple expression linking the polynomials C-n((lambda)) and C-n((1/2-lambda-n)) and show how to derive various properties of the zeros of C-n((lambda)) when A < 1 n from properties of the zeros of C-n((lambda)) when lambda > -1/2. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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