论文标题
Chebyshev多项式的二项式组合的零
Zeros of a binomial combination of Chebyshev polynomials
论文作者
论文摘要
对于$ 0 <α<1 $，我们研究了多项式$ \ left \ weft \ {m}（z）\ right \} _ {m = 0}^{\ infty} $生成的零{p_ {m}（z）\ right \} _ {p_ {m}（z）（z）（z）（z）（z）_ {p_ {m}（z）_ {p_ {m}（z）$，由$（1-t）^$（1-t）^al $ ate $ aige as aige as aiged as aigy as a，同等地，该序列是从系数具有二项式形式的Chebyshev多项式的线性组合获得的。我们表明，$ p_ {m}（z）$的零数在间隔$（-1,1）$之外由$ m $的常数独立。
For $0<α<1$, we study the zeros of the sequence of polynomials $\left\{ P_{m}(z)\right\} _{m=0}^{\infty}$ generated by the reciprocal of $(1-t)^α(1-2zt+t^{2})$, expanded as a power series in $t$. Equivalently, this sequence is obtained from a linear combination of Chebyshev polynomials whose coefficients have a binomial form. We show that the number of zeros of $P_{m}(z)$ outside the interval $(-1,1)$ is bounded by a constant independent of $m$.
