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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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On some orthogonal polynomial integrals
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by Luigi Gatteschi PDF
Math. Comp. 35 (1980), 1291-1298 Request permission

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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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 35 (1980), 1291-1298
  • MSC: Primary 33A65
  • DOI: https://doi.org/10.1090/S0025-5718-1980-0583506-X
  • MathSciNet review: 583506