Nearest Neighbor Recurrence Relations for Meixner–Angelesco Multiple Orthogonal Polynomials of the Second Kind
This paper studies a new family of Angelesco multiple orthogonal polynomials with shared orthogonality conditions with respect to a system of weight functions, which are complex analogs of Pascal distributions on a legged star-like set. The emphasis is placed on the algebraic properties, such as the...
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| Published in: | Mathematics (Basel) Vol. 12; no. 1; p. 62 |
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| Abstract | This paper studies a new family of Angelesco multiple orthogonal polynomials with shared orthogonality conditions with respect to a system of weight functions, which are complex analogs of Pascal distributions on a legged star-like set. The emphasis is placed on the algebraic properties, such as the raising operators, the Rodrigues-type formula, the explicit expression of the polynomials, and the nearest neighbor recurrence relations. |
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| AbstractList | This paper studies a new family of Angelesco multiple orthogonal polynomials with shared orthogonality conditions with respect to a system of weight functions, which are complex analogs of Pascal distributions on a legged star-like set. The emphasis is placed on the algebraic properties, such as the raising operators, the Rodrigues-type formula, the explicit expression of the polynomials, and the nearest neighbor recurrence relations. |
| Audience | Academic |
| Author | Arvesú, Jorge Quintero Roba, Alejandro J. |
| Author_xml | – sequence: 1 givenname: Jorge orcidid: 0000-0002-0577-4297 surname: Arvesú fullname: Arvesú, Jorge – sequence: 2 givenname: Alejandro J. surname: Quintero Roba fullname: Quintero Roba, Alejandro J. |
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| Cites_doi | 10.1016/j.jat.2019.105324 10.1016/S0377-0427(02)00597-6 10.1088/1751-8113/46/50/505201 10.1007/s00365-019-09457-2 10.1016/S0377-0427(98)00175-7 10.1016/j.jat.2011.05.003 10.1007/978-3-642-05014-5 10.4064/-24-1-51-84 10.1088/1751-8113/45/32/325205 10.1007/BFb0076532 10.1016/j.jmaa.2013.09.057 10.1007/978-3-642-74748-9 |
| ContentType | Journal Article |
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| References | Leurs (ref_13) 2020; 51 Mahler (ref_22) 1968; 19 Angelesco (ref_20) 1919; 168 Aptekarev (ref_5) 1998; 99 Bhatia (ref_16) 2010; Volume 3 Assche (ref_18) 2011; 136 Sorokin (ref_21) 1986; 41 ref_12 ref_11 Coussement (ref_9) 2003; 153 ref_1 Miki (ref_10) 2012; 45 Aptekarev (ref_15) 2014; 411 ref_2 Sorokin (ref_3) 1984; 8 (ref_17) 2015; 11 ref_19 (ref_23) 2020; 32 Leurs (ref_14) 2020; 250 ref_8 ref_4 Brezinski (ref_6) 1994; Volume 119 Brezinski (ref_7) 1985; Volume 1171 |
| References_xml | – volume: 250 start-page: 105324 year: 2020 ident: ref_14 article-title: Laguerre-Angelesco multiple orthogonal polynomials on an r-star publication-title: J. Approx. Theory doi: 10.1016/j.jat.2019.105324 contributor: fullname: Leurs – volume: 19 start-page: 95 year: 1968 ident: ref_22 article-title: Perfect systems publication-title: Compos. Math. contributor: fullname: Mahler – volume: Volume 119 start-page: 29 year: 1994 ident: ref_6 article-title: Vector orthogonal polynomials of dimension d publication-title: Approximation and Computation: A Festschrift in Honor of Walter Gautschi: Proceedings of the Purdue Conference, West Lafayette, IN, USA, 2–5 December 1993 contributor: fullname: Brezinski – ident: ref_4 – volume: 153 start-page: 19 year: 2003 ident: ref_9 article-title: Some discrete multiple orthogonal polynomials publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(02)00597-6 contributor: fullname: Coussement – ident: ref_2 – ident: ref_12 – volume: 32 start-page: 361 year: 2020 ident: ref_23 article-title: Multiple q-Kravchuk polynomials publication-title: Integral Transform. Spec. Funct. – volume: 8 start-page: 45 year: 1984 ident: ref_3 article-title: Simultaneous Padé approximants for finite and infinite intervals publication-title: Izv. Vyssh. Uchebn. Zaved. Mat. contributor: fullname: Sorokin – ident: ref_11 doi: 10.1088/1751-8113/46/50/505201 – volume: 51 start-page: 353 year: 2020 ident: ref_13 article-title: Jacobi-Angelesco multiple orthogonal polynomials on an r-star publication-title: Constr. Approx. doi: 10.1007/s00365-019-09457-2 contributor: fullname: Leurs – volume: 99 start-page: 423 year: 1998 ident: ref_5 article-title: Multiple orthogonal polynomials publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(98)00175-7 contributor: fullname: Aptekarev – volume: 136 start-page: 1427 year: 2011 ident: ref_18 article-title: Nearest neighbor recurrence relations for multiple orthogonal polynomials publication-title: J. Approx. Theory doi: 10.1016/j.jat.2011.05.003 contributor: fullname: Assche – ident: ref_19 doi: 10.1007/978-3-642-05014-5 – ident: ref_8 doi: 10.4064/-24-1-51-84 – volume: 45 start-page: 325205 year: 2012 ident: ref_10 article-title: An algebraic model for the multiple Meixner polynomials of the first kind publication-title: J. Phys. A Math. Theor. doi: 10.1088/1751-8113/45/32/325205 contributor: fullname: Miki – volume: 168 start-page: 262 year: 1919 ident: ref_20 article-title: Sur deux extensions des fractions continues algébriques publication-title: Comptes Rendus Acad. Sci. contributor: fullname: Angelesco – volume: 41 start-page: 245 year: 1986 ident: ref_21 article-title: A generalization of Laguerre polynomials and convergence of simultaneous Padé approximants publication-title: Uspekhi Mat. Nauk contributor: fullname: Sorokin – volume: Volume 1171 start-page: 74 year: 1985 ident: ref_7 article-title: Simultaneous Padé approximation and orthogonality publication-title: Polynômes Orthogonaux et Applications doi: 10.1007/BFb0076532 contributor: fullname: Brezinski – volume: 411 start-page: 485 year: 2014 ident: ref_15 article-title: Asymptotics for multiple Meixner polynomials publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2013.09.057 contributor: fullname: Aptekarev – volume: Volume 3 start-page: 1417 year: 2010 ident: ref_16 article-title: Multiple orthogonal polynomials in random matrix theory publication-title: Proceedings of the International Congress of Mathematicians contributor: fullname: Bhatia – ident: ref_1 doi: 10.1007/978-3-642-74748-9 – volume: 11 start-page: 026 year: 2015 ident: ref_17 article-title: On the q-Charlier Multiple Orthogonal Polynomial publication-title: SIGMA |
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| SubjectTerms | Analysis Angelesco polynomials Approximation Binomial distribution classical orthogonal polynomials discrete orthogonal polynomials Functions, Orthogonal Mathematical analysis Meixner polynomials multiple orthogonal polynomials Operators (mathematics) Orthogonality Polynomials Rodrigues-type formula Weighting functions |
| Title | Nearest Neighbor Recurrence Relations for Meixner–Angelesco Multiple Orthogonal Polynomials of the Second Kind |
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