Some properties of orthogonal polynomials

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 ${q_n}(x) = \smallint _{ - 1}^1w(t){p_n}(t){(x - t)^{ - 1}}dt$.