Some orthogonal polynomials on the finite interval and Gaussian quadrature rules for fractional Riemann‐Liouville integrals

Some orthogonal polynomials on the finite interval and Gaussian quadrature rules for fractional Riemann‐Liouville integrals

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 th...

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Veröffentlicht in:Mathematical methods in the applied sciences 2021-01, Vol.44 (1), p.493-516
1. Verfasser: Milovanović, Gradimir V.
Format: Artikel
Sprache:eng
Schlagworte:
Gaussian quadrature rule
Integrals
Numerical analysis
orthogonal polynomials
Polynomials
Quadratures
Riemann‐Liouville fractional integral
three‐term recurrence relation
weight function
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Zusammenfassung: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6752