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Some orthogonal polynomials on the finite interval and Gaussian quadrature rules for fractional Riemann‐Liouville integrals
Author(s) -
Milovanović Gradimir V.
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6752
Subject(s) - mathematics , gaussian quadrature , orthogonal polynomials , quadrature (astronomy) , gaussian , gauss–jacobi quadrature , computation , clenshaw–curtis quadrature , numerical integration , mathematical analysis , type (biology) , pure mathematics , nyström method , integral equation , algorithm , computational chemistry , engineering , electrical engineering , chemistry , ecology , biology
Inspired with papers by Bokhari, Qadir, and Al‐Attas (2010) and by Rapaić, Šekara, and Govedarica (2014), in this paper we investigate a few types of orthogonal polynomials on finite intervals and derive the corresponding quadrature formulas of Gaussian type for efficient numerical computation of the left and right fractional Riemann‐Liouville integrals. Several numerical examples are included to demonstrate the numerical efficiency of the proposed procedure.