On the Roots of Orthogonal Polynomials and Euler-Frobenius Polynomials
On the Roots of Orthogonal Polynomials and Euler-Frobenius Polynomials
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论正交多项式和欧拉-弗罗贝尼乌斯多项式的根
DOI：
10.1006/jmaa.1995.1399
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
J. Savoie
中科院分区：
文献类型：
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作者：
F. Dubeau;J. Savoie
文摘交错多项式的根的性质P n (x)和P n + 1 (x)和P (x)和P n + 2 (x)获得了序列生成多项式的递归的方案:P (x) = 0 x l非负整数(l)和c n + 1 P n + 1 (x) =−2 r n x P (x) +(1−x 2) DP n (x)。超球面多项式和欧拉-弗洛贝尼乌斯多项式就是这种序列的例子。对于类Hermite多项式，我们得到了类似的结果：h0 (x) = xl （l是一个非负整数）和hn +1 (x) = - 2 xhn (x) + DH n (x)。
Abstract Interlacing properties of the roots of the polynomials P n ( x ) and P n +1 ( x ) and P n ( x ) and P n +2 ( x ) are obtained for sequences of polynomials generated recursively by the scheme: P 0 ( x ) = x l ( l a nonnegative integer) and c n +1 P n +1 ( x ) = −2 r n x P n ( x ) + (1 − x 2 ) DP n ( x ). Ultraspherical polynomials and Euler-Frobenius polynomials are examples of such sequences. We obtain similar results for Hermite like polynomials obtained by the scheme: H 0 ( x ) = x l ( l a nonnegative integer) and H n +1 ( x ) = −2 xH n ( x ) + DH n ( x ).