On the zeros of certain linear combinations of Chebyshev polynomials
نویسندگان
چکیده
منابع مشابه
On Linear Combinations of Chebyshev Polynomials
a0Tn(x) + a1Tn−1(x) + · · ·+ amTn−m(x) where (a0, a1, . . . , am) is a fixed m-tuple of real numbers, a0, am 6= 0, Ti(x) are Chebyshev polynomials of the first kind, n = m, m + 1, m + 2, . . . Here we analyze the structure of the set of zeros of such polynomial, depending on A and its limit points when n tends to infinity. Also the expression of envelope of the polynomial is given. An applicati...
متن کاملon the effect of linear & non-linear texts on students comprehension and recalling
چکیده ندارد.
15 صفحه اولZeros of linear combinations of Laguerre polynomials from different sequences
We study interlacing properties of the zeros of two types of linear combinations of Laguerre polynomials with different parameters, namely Rn = L α n + aL α n and Sn = L α n + bL α n−1. Proofs and numerical counterexamples are given in situations where the zeros of Rn, and Sn, respectively, interlace (or do not in general) with the zeros of L α k , L ′ k , k = n or n− 1. The results we prove ho...
متن کاملThe Zeros of Certain Composite Polynomials
we may obtain various theorems on the relative location of the zeros of A 0(2) and An(z) by the familiar method of first finding such relations for two successive Ak{z) and then iterating the relations n times. This method has already been employed in the study of the zeros of sequence (1.1) for the following three cases: (1) for all k, Pk = 0 and yk is real; 1 (2) for all k, yk~m + l—a limitin...
متن کاملOn the Location of the Zeros of Certain Polynomials
Abstract. We extend Aziz and Mohammad’s result that the zeros, of a polynomial P (z) = ∑n j=0 ajz , taj > aj−1 > 0, j = 2, 3, . . . , n for certain t ( > 0), with moduli greater than t(n − 1)/n are simple, to polynomials with complex coefficients. Then we improve their result that the polynomial P (z), of degree n, with complex coefficients, does not vanish in the disc |z − ae| < a/(2n); a > 0,...
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 Computational and Applied Mathematics
سال: 1995
ISSN: 0377-0427
DOI: 10.1016/0377-0427(95)00098-4