Upper bounds for the zeros of ultraspherical polynomials
نویسندگان
چکیده
منابع مشابه
Bounds for Extreme Zeros of Quasi–orthogonal Ultraspherical Polynomials
We discuss and compare upper and lower bounds obtained by two different methods for the positive zero of the ultraspherical polynomial C n that is greater than 1 when −3/2 < λ <−1/2. Our first approach uses mixed three term recurrence relations and interlacing of zeros while the second approach uses a method going back to Euler and Rayleigh and already applied to Bessel functions and Laguerre a...
متن کاملBounds for Zeros of the Charlier Polynomials
We use the method of positive quadratic forms and discrete analogues of the Laguerre inequality recently obtained by the author, to give bounds on the zeros of the Charlier polynomials, which are uniform in all parameters involved.
متن کاملOn a Separation Theorem for the Zeros of the Ultraspherical Polynomials
1. It will be recalled that the ultraspherical polynomials are those which are orthogonal on the interval ( — 1, 1), corresponding to the weight function (1— x2)x~1/2, X>—1/2. In what follows X = 0 will also be excluded. The coefficients of these polynomials are functions of the parameter X appearing in the weight function, and the symbol P„(x, X), indicative of this fact, will be used to denot...
متن کاملOn Bounds For The Zeros of Univariate Polynomials
Problems on algebraical polynomials appear in many fields of mathematics and computer science. Especially the task of determining the roots of polynomials has been frequently investigated. Nonetheless, the task of locating the zeros of complex polynomials is still challenging. In this paper we deal with the location of zeros of univariate complex polynomials. We prove some novel upper bounds fo...
متن کاملSome compact generalization of inequalities for polynomials with prescribed zeros
Let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$. In this paper we obtain some new results about the dependence of $|p(Rz)|$ on $|p(rz)| $ for $r^2leq rRleq k^2$, $k^2 leq rRleq R^2$ and for $Rleq r leq k$. Our results refine and generalize certain well-known polynomial inequalities.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1990
ISSN: 0021-9045
DOI: 10.1016/0021-9045(90)90025-l