Inequalities for the zeros of Legendre polynomials and related functions
نویسندگان
چکیده
منابع مشابه
Some 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.
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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.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1936
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1936-1501831-2