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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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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DOI: http://dx.doi.org/10.1090/S0025-5718-1980-0583506-X
PII: S 0025-5718(1980)0583506-X
Article copyright: © Copyright 1980 American Mathematical Society