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Mathematics of Computation

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On some orthogonal polynomial integrals

Author: Luigi Gatteschi
Journal: Math. Comp. 35 (1980), 1291-1298
MSC: Primary 33A65
MathSciNet review: 583506
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Abstract: The modified moments of the weight functions $w(x) = {x^\rho }{(1 - x)^a}\ln (1/x)$, on [0, 1], with respect to the shifted Jacobi polynomials $P_n^{\ast (\alpha ,\beta )}(x) = P_n^{(\alpha ,\beta )}(2x - 1)$, and ${w_p}(x) = {x^\rho }{e^{ - x}}{(\ln x)^p}$, $p = 1,2$, on $[0,\infty )$, with respect to the generalized La guerre polynomials $L_n^{(\alpha )}(x)$, are explicitly evaluated.

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Article copyright: © Copyright 1980 American Mathematical Society