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## Assche, Multiple orthogonal polynomials for classical weights

Venue: | MR1990569 (2004g:33014) Licensed to Penn St Univ, University Park. Prepared on Fri Jul 5 09:17:03 EDT 2013 for download from IP 130.203.136.75. License |

Citations: | 55 - 4 self |

### Citations

133 |
Rational Approximations and Orthogonality,
- Nikishin, Sorokin
- 1991
(Show Context)
Citation Context ...tical Society License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use3888 A. I. APTEKAREV, A. BRANQUINHO, AND W. VAN ASSCHE survey papers [1], [4], =-=[12]-=-, [13], [16], [18]). In [4] a classification was given of multiple orthogonal polynomials with respect to semiclassical weights of class s ≥ 1, where s =max{deg φ−2 , deg ψ −1}, and the weights for th... |

60 |
A note on the irrationality of ζ (2) and ζ (3)
- Beukers
- 1979
(Show Context)
Citation Context ...ities. Polynomials obtained by means of a product of Rodrigues operators appear for instance in irrationality proofs, such as the irrationality of π 2 and ζ(3). See, for instance, [6, Appendix 2] and =-=[5]-=- where such polynomials are disguised by several integrations by part, and [15], [16]. In Section 3 we present explicit formulas for the polynomials from Tables 1 and 2 and for the recurrence coeffici... |

39 | Some classical multiple orthogonal polynomials,
- Assche, Coussement
- 2001
(Show Context)
Citation Context ...nse or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use3888 A. I. APTEKAREV, A. BRANQUINHO, AND W. VAN ASSCHE survey papers [1], [4], [12], [13], [16], =-=[18]-=-). In [4] a classification was given of multiple orthogonal polynomials with respect to semiclassical weights of class s ≥ 1, where s =max{deg φ−2 , deg ψ −1}, and the weights for the orthogonality re... |

33 | Aptekarev, Multiple orthogonal polynomials, - I - 1998 |

28 | Classical orthogonal polynomials: a functional approach - Marcellán, Branquinho, et al. - 1994 |

27 |
Assche, Multiple orthogonal polynomials, irrationality and transcendence, Continued Fractions: From Analytic Number Theory to Constructive Approximation
- Van
- 1998
(Show Context)
Citation Context ...y License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use3888 A. I. APTEKAREV, A. BRANQUINHO, AND W. VAN ASSCHE survey papers [1], [4], [12], [13], =-=[16]-=-, [18]). In [4] a classification was given of multiple orthogonal polynomials with respect to semiclassical weights of class s ≥ 1, where s =max{deg φ−2 , deg ψ −1}, and the weights for the orthogonal... |

24 | Iseghem, The genetic sum’s representation for the moments of a system of Stieltjes functions and its applications, Constr
- Aptekarev, Kalyagin, et al.
(Show Context)
Citation Context .../journal-terms-of-useMULTIPLE ORTHOGONAL POLYNOMIALS 3889 φ Table 2. {wk} p k=1 Case z zα exp(βkz) Laguerre II 1 exp(δ/2z2 + βkz) Hermite given in Table 1 was studied by L. Piñeiro (cf. [11]) and in =-=[3]-=-, [18]; the case of Laguerre I polynomials was considered by V. N. Sorokin in [14] and in [18]; Laguerre II polynomials appeared in [12] and [18]; multiple Hermite polynomials were mentioned in [18]. ... |

10 |
The operator moment problem, vector continued fractions and an explicit form of the Favard theorem for vector orthogonal polynomials
- Kaliaguine
- 1995
(Show Context)
Citation Context ...he Bogoyavlenskii lattice ([2], [9], [17]). The existence of such a type of recurrence relation for general multiple orthogonal polynomials in the diagonal case (n1 = n2 = ···= np) was proven in [9], =-=[10]-=-. In Section 4 we prove our main result (Theorems 2 and 3) that these systems of multiple orthogonal polynomials satisfy an ordinary linear differential equation of order p + 1 with polynomial coeffic... |

7 |
On simultaneous approximations for a collection of Markov functions, Vestnik Moskov
- Piñeiro
- 1987
(Show Context)
Citation Context ...//www.ams.org/journal-terms-of-useMULTIPLE ORTHOGONAL POLYNOMIALS 3889 φ Table 2. {wk} p k=1 Case z zα exp(βkz) Laguerre II 1 exp(δ/2z2 + βkz) Hermite given in Table 1 was studied by L. Piñeiro (cf. =-=[11]-=-) and in [3], [18]; the case of Laguerre I polynomials was considered by V. N. Sorokin in [14] and in [18]; Laguerre II polynomials appeared in [12] and [18]; multiple Hermite polynomials were mention... |

7 |
Hermite-Padé approximations for Nikishin systems and the irrationality of ζ(3
- Sorokin
- 1994
(Show Context)
Citation Context ...r for instance in irrationality proofs, such as the irrationality of π 2 and ζ(3). See, for instance, [6, Appendix 2] and [5] where such polynomials are disguised by several integrations by part, and =-=[15]-=-, [16]. In Section 3 we present explicit formulas for the polynomials from Tables 1 and 2 and for the recurrence coefficients of the four-term recurrence relation when p =2. Multiple orthogonal polyno... |

6 |
Semiclassical multiple orthogonal polynomials and the properties of Jacobi-Bessel polynomials,
- Aptekarev, Marcellan, et al.
- 1997
(Show Context)
Citation Context ...thematical Society License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use3888 A. I. APTEKAREV, A. BRANQUINHO, AND W. VAN ASSCHE survey papers [1], =-=[4]-=-, [12], [13], [16], [18]). In [4] a classification was given of multiple orthogonal polynomials with respect to semiclassical weights of class s ≥ 1, where s =max{deg φ−2 , deg ψ −1}, and the weights ... |

6 |
Simultaneous Padé approximation for functions of Stieltjes type, Sib.Mat
- Sorokin
- 1990
(Show Context)
Citation Context ...Case z zα exp(βkz) Laguerre II 1 exp(δ/2z2 + βkz) Hermite given in Table 1 was studied by L. Piñeiro (cf. [11]) and in [3], [18]; the case of Laguerre I polynomials was considered by V. N. Sorokin in =-=[14]-=- and in [18]; Laguerre II polynomials appeared in [12] and [18]; multiple Hermite polynomials were mentioned in [18]. Most of the examples above first appeared in the context of simultaneous rational ... |

5 |
Complex rational approximation and difference
- Aptekarev, Kaliaguine
- 1998
(Show Context)
Citation Context ...ry of nonsymmetric difference operators and the corresponding nonlinear dynamical systems, like the higher-order non-symmetric generalization of the Toda lattice, known as the Bogoyavlenskii lattice (=-=[2]-=-, [9], [17]). The existence of such a type of recurrence relation for general multiple orthogonal polynomials in the diagonal case (n1 = n2 = ···= np) was proven in [9], [10]. In Section 4 we prove ou... |

5 |
Hermite-Padé approximants and spectral analysis of nonsymmetric operators
- Kalyagin
- 1994
(Show Context)
Citation Context ... nonsymmetric difference operators and the corresponding nonlinear dynamical systems, like the higher-order non-symmetric generalization of the Toda lattice, known as the Bogoyavlenskii lattice ([2], =-=[9]-=-, [17]). The existence of such a type of recurrence relation for general multiple orthogonal polynomials in the diagonal case (n1 = n2 = ···= np) was proven in [9], [10]. In Section 4 we prove our mai... |

3 |
Assche, Non-symmetric linear difference equations for multiple orthogonal polynomials
- Van
- 2000
(Show Context)
Citation Context ...ymmetric difference operators and the corresponding nonlinear dynamical systems, like the higher-order non-symmetric generalization of the Toda lattice, known as the Bogoyavlenskii lattice ([2], [9], =-=[17]-=-). The existence of such a type of recurrence relation for general multiple orthogonal polynomials in the diagonal case (n1 = n2 = ···= np) was proven in [9], [10]. In Section 4 we prove our main resu... |

2 | A note on semi-classical orthogonal polynomials - Branquinho - 1996 |

1 |
Generalization of classical polynomials and convergence of simultaneous Padé approximants, Trudy Sem
- Sorokin
- 1986
(Show Context)
Citation Context ...Society License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use3888 A. I. APTEKAREV, A. BRANQUINHO, AND W. VAN ASSCHE survey papers [1], [4], [12], =-=[13]-=-, [16], [18]). In [4] a classification was given of multiple orthogonal polynomials with respect to semiclassical weights of class s ≥ 1, where s =max{deg φ−2 , deg ψ −1}, and the weights for the orth... |