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Mathematics of Computation

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Some properties of orthogonal polynomials

Author: D. B. Hunter
Journal: Math. Comp. 29 (1975), 559-565
MSC: Primary 42A52
MathSciNet review: 0374792
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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) = \smallint _{ - 1}^1w(t){p_n}(t){(x - t)^{ - 1}}dt$.

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Keywords: Orthogonal polynomials, weight-function, power-series, Jacobi polynomials, Gaussian quadrature
Article copyright: © Copyright 1975 American Mathematical Society

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