On some orthogonal polynomial integrals
HTML articles powered by AMS MathViewer
- 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.References
- Richard Askey and Behzad Razban, An integral for Jacobi polynomials, Simon Stevin 46 (1972/73), 165–169. MR 328160
- James L. Blue, A Legendre polynomial integral, Math. Comp. 33 (1979), no. 146, 739–741. MR 521287, DOI 10.1090/S0025-5718-1979-0521287-8
- James L. Blue, A Legendre polynomial integral, Math. Comp. 33 (1979), no. 146, 739–741. MR 521287, DOI 10.1090/S0025-5718-1979-0521287-8 G. SZEGÖ, Orthogonal Polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R. I., 1975.
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