Positivity of Turán Determinants for Orthogonal Polynomials
Positivity of Turán Determinants for Orthogonal Polynomials
复制标题
正交多项式的 Turán 行列式的正性
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
R. Szwarc
中科院分区：
文献类型：
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作者：
R. Szwarc
若Pn 2(X)-Pn-1(X)Pn+1(X)≥0为≥1，且对正交区间内的所有x都满足Turan不等式，则正交多项式pn满足Turan不等式.给出了满足Turan不等式的正交多项式的一般判据。这给出了经典正交多项式的已知结果和新的结果，例如q-超球面多项式。
The orthogonal polynomials p n satisfy Turan’s inequality if pn 2(x)-pn-1(x)pn+1(x) ≥ 0 for ≥ 1 and for all x in the interval of orthogonality. We give general criteria for orthogonal polynomials to satisfy Turan’s inequality. This yields the known results for classical orthogonal polynomials as well as new results, for example, for the q-ultraspherical polynomials.