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Some Properties of Orthogonal Polynomials

D. B. Hunter
Mathematics of Computation
Vol. 29, No. 130 (Apr., 1975), pp. 559-565
DOI: 10.2307/2005575
Stable URL: http://www.jstor.org/stable/2005575
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Some Properties of Orthogonal Polynomials
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Abstract

Some results are obtained concerning the signs of the coefficients in the expansions in powers of $x^{-1}, (1 + x)^{-1}$ or $(1 - x)^{-1}$ of $1/p_n(x)$ and $q_n(x)$, where $p_n(x)$ is the polynomial of degree $n$ in the orthogonal sequence associated with a given weight-function $w(x)$ over $(-1, 1)$ and $q_n(x) = \int^1_{-1}w(t)p_n(t)(x - t)^{-1} dt$.

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