Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A monotonic property for the zeros of ultraspherical polynomials

Author: Andrea Laforgia
Journal: Proc. Amer. Math. Soc. 83 (1981), 757-758
MSC: Primary 33A45; Secondary 34C10
MathSciNet review: 630050
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that $ \lambda x_{n,k}^{(\lambda )}$ increases as $ \lambda $ increases for $ 0 < \lambda < 1,k = 1,2, \ldots ,\left[ {\tfrac{n}{2}} \right] $, where $ x_{n,k}^{(\lambda )}$ is the $ k{\text{th}}$ positive zero of ultraspherical polynomial $ P_n^{(\lambda )}(x)$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 33A45, 34C10

Retrieve articles in all journals with MSC: 33A45, 34C10

Additional Information

Keywords: Zeros of ultraspherical polynomials, Sturm comparison theorem
Article copyright: © Copyright 1981 American Mathematical Society