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On the Monotonic Variation of the Zeros of Ultraspherical Polynomials with the Parameters

Published online by Cambridge University Press:  20 November 2018

Renato Spigler
Renato Spigler*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, New York 10012
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Abstract

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We show that increases with λ, for 0< λ < 1, being the kth zero of the ultraspherical polynomial and f(λ) a suitable function of λ. As a consequence, some inequalities for and an estimate for can be obtained.

Keywords

33A4534A50zeros of ultraspherical polynomialsSturm comparison theorem
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 4 , 01 December 1984 , pp. 472 - 477
Copyright
Copyright © Canadian Mathematical Society 1984

Footnotes

(2)

On leave from the University of Padua, Italy.

(1)

This work was supported, in part, by the Italian C.N.R.

References

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3. Laforgia, A., A monotonie property for the zeros of ultraspherical polynomials, Proc. Amer. Math. Soc, 83 (1981), 757-758.CrossRefGoogle Scholar
4. Szegö, G., Orthogonal Polynomials, 4th éd., Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc, Providence, R. I., 1975.Google Scholar