Connections between two-variable Bernstein and Jacobi polynomials on the triangle

Connections between two-variable Bernstein and Jacobi polynomials on the triangle

Connection coefficients between the two-variable Bernstein and Jacobi polynomial families on the triangle are given explicitly as evaluations of two-variable Hahn polynomials. Dual two-variable Bernstein polynomials are introduced. Explicit formula in terms of two-variable Jacobi polynomials and a r...

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Veröffentlicht in:Journal of computational and applied mathematics 2006-12, Vol.197 (2), p.520-533
Hauptverfasser: Lewanowicz, Stanisław, Woźny, Paweł
Format: Artikel
Sprache:eng
Schlagworte:
Connection relations
Difference and functional equations, recurrence relations
Dual two-variable Bernstein polynomials
Exact sciences and technology
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Special functions
Two-variable Bernstein polynomials
Two-variable Hahn polynomials
Two-variable Jacobi polynomials
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Beschreibung
Zusammenfassung:Connection coefficients between the two-variable Bernstein and Jacobi polynomial families on the triangle are given explicitly as evaluations of two-variable Hahn polynomials. Dual two-variable Bernstein polynomials are introduced. Explicit formula in terms of two-variable Jacobi polynomials and a recurrence relation are given.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2005.11.013