Geodesic
On Linear Combinations of Chebyshev Polynomials
Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 57 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

We investigate an infinite sequence of polynomials of the form: $ a_0T_n(x)+a_1T_{n-1}(x)+\dots+a_mT_{n-m}(x) $ where $(a_0,a_1,\ldots,a_m)$ is a fixed $m$-tuple of real numbers, $a_0,a_m\neq0$, $T_i(x)$ are Chebyshev polynomials of the first kind, $n=m,m+1,m+2,\ldots$ 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 application in number theory, more precise, in the theory of Pisot and Salem numbers is presented.
DOI : 10.2298/PIM150220001S
Classification : 11B83 11R09,12D10
Keywords: Chebyshev polynomials, envelope, Pisot numbers, Salem numbers 
@article{10_2298_PIM150220001S,
     author = {Dragan Stankov},
     title = {On {Linear} {Combinations} of {Chebyshev} {Polynomials}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {57 },
     publisher = {mathdoc},
     volume = {_N_S_97},
     number = {111},
     year = {2015},
     doi = {10.2298/PIM150220001S},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM150220001S/}
}
TY  - JOUR
AU  - Dragan Stankov
TI  - On Linear Combinations of Chebyshev Polynomials
JO  - Publications de l'Institut Mathématique
PY  - 2015
SP  - 57 
VL  - _N_S_97
IS  - 111
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2298/PIM150220001S/
DO  - 10.2298/PIM150220001S
LA  - en
ID  - 10_2298_PIM150220001S
ER  - 
%0 Journal Article
%A Dragan Stankov
%T On Linear Combinations of Chebyshev Polynomials
%J Publications de l'Institut Mathématique
%D 2015
%P 57 
%V _N_S_97
%N 111
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2298/PIM150220001S/
%R 10.2298/PIM150220001S
%G en
%F 10_2298_PIM150220001S
Dragan Stankov. On Linear Combinations of Chebyshev Polynomials. Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 57 . doi : 10.2298/PIM150220001S. http://geodesic.mathdoc.fr/articles/10.2298/PIM150220001S/

Cité par Sources :