Some classical multiple orthogonal polynomials
By Walter Van Assche, Els Coussement. 2001
161 citations recorded by the source corpus.
Recently there has been a renewed interest in an extension of the notion of orthogonal polynomials known as multiple orthogonal polynomials. This notion comes from simultaneous rational approximation (Hermite-Pade approximation) of a system of several functions. We describe seven families of multiple orthogonal polynomials which have he same flavor as the very classical orthogonal polynomials of Jacobi, Laguerre and Hermite. We also mention some open research problems and some applications.
Subfields: Algebra and Number Theory, Applied Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/3362a6d54b69f8a32e451f058f1de37b7ce7f082
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In Algebra and Number Theory
- Arno B. J. Kuijlaars
- Pavel Bleher
- Walter Van Assche
- J. Coussement
- J. Arvesú
- Alexander I. Aptekarev
- K. Mclaughlin
- Andrei Martínez-Finkelshtein
In Applied Mathematics
- Arno B. J. Kuijlaars
- Pavel Bleher
- Walter Van Assche
- J. Coussement
- J. Arvesú
- Ali Zaghouani
- Youssèf Ben Cheikh
- Alexander I. Aptekarev
In Numerical Analysis
Citations in the corpus
- Some discrete multiple orthogonal polynomials (2003, methodology): “II with nearly diagonal multi-indices [ 10 ].”
- Multiple orthogonal polynomial ensembles (2009, background): “e-Pad´e approximation and in this context they are also called Hermite-Pad´e polynomials [2, 4, 20, 33, 34, 40, 41, 42, 52, 60]. MOPs were also studied from the point of view of new special functions [6, 19, 22, 49, 64, 67]. See the books [44, 59] and the survey papers [3, 8, 65, 66] for these aspec”
- Some discrete d -orthogonal polynomial sets (2003, background): “The continuous case was studied, for instance, in [3,4,14,25,26].”
- Large n Limit of Gaussian Random Matrices with External Source, Part I (2004, background): “2) The polynomial Pn1,n2(x) is unique and it is called a multiple Hermite polynomial, see [2, 25].”