Recurrence coefficients of generalized Meixner polynomials and Painlevé equations

Journal of Physics A: Mathematical and Theoretical

Volumn 44, Issue 3, 2011, Pages

  Boelen, Lies ^a   Filipuk, Galina ^b   Van Assche, Walter ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78751486416     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/44/3/035202     Document Type: Article

References (35)

1. Abramowitz M and Stegun I 1965 Handbook of Mathematical Functions (New York: Dover)
2. Basor E and Chen Y 2009 Painlevé V and the distribution function of a discontinuous linear statistic in the Laguerre unitary ensembles J. Phys. A: Math. Theor. 42 035203
3. Basor E, Chen Y and Ehrhardt T 2010 Painlevé V and time-dependent Jacobi polynomials J. Phys. A: Math. Theor. 43 015204
4. Boelen L 2010 Discrete Painlevé equations and orthogonal polynomials PhD Thesis Katholieke Universiteit Leuven
5. Chen Y and Feigin M V 2006 Painlevé IV and degenerate Gaussian unitary ensembles J. Phys. A: Math. Gen. 39 12381-93
6. Chen Y and Its A 2010 Painlevé III and a singular linear statistics in Hermitian random matrix ensembles: I J. Approx. Theory 162 270-97
7. Chen Y and Zhang L 2010 Painlevé VI and the unitary Jacobi ensembles Stud. Appl. Math. 125 91-112 (arXiv:0911.5636)
8. Chen Y and Dai D 2010 Painlevé V and a Pollaczek-Jacobi type orthogonal polynomials J. Approx. Theory 162 2149-67 (arXiv:0809.3641)
9. Chihara T S 1978 An Introduction to Orthogonal Polynomials (New York: Gordon and Breach)
10. Clarkson P A 2006 Painlevé Equations-Nonlinear Special Functions (Lecture Notes in Mathematics vol 1883) (Berlin: Springer) pp 331-411
11. Cosgrove C M 2006 Chazy's second-degree Painlevé equations J. Phys. A: Math. Gen. 39 11955-71
12. Fokas A S, Its A R and Kitaev A V 1991 Discrete Painlevé equations and their appearance in quantum gravity Commun. Math. Phys. 142 313-44
13. Freud G 1976 On the coefficients in the recursion formulae of orthogonal polynomials Proc. R. Irish Acad. A 76 1-6
14. Gambier B 1910 Sur les équations différentielles du second ordre et du premier degré dont l'intégrale générale est à points critiques fixés Acta Math. 33 1-55
15. Grammaticos B and Ramani A 1996 Discrete Painlevé equations: coalescences, limits and degeneracies Physica A 228 160-71
16. Grammaticos B and Ramani A 2004 Discrete Painlevé Equations: A Review (Lecture Notes Physics vol 644) (Berlin: Springer) pp 245-321
17. Grammaticos B, Ramani A and Papageorgiou V 1991 Do integrable mappings have the Painlevé property? Phys. Rev. Lett. 67 1825-8
18. Ronveaux A 1986 Discrete semi-classical orthogonal polynomials: generalized Meixner J. Approx. Theory 46 403-7
19. Ronveaux A 2001 Asymptotics for recurrence coefficients of the generalized Meixner case J. Comput. Appl. Math. 133 695-6
20. Gromak V I, Laine I and Shimomura S 2002 Painlevé Differential Equations in the Complex Plane (Studies in Mathematics vol 28) (Berlin, New York: de Gruyter & Co)
21. Hendriksen E and van Rossum H 1985 Semi-classical orthogonal polynomials Polynômes Orthogonaux et Applications (Lecture Notes in Mathematics vol 1171) (Berlin: Springer) pp 354-61
22. Hahn W 1935 Über die Jacobischen Polynome und zwei verwante Polynomklassen Math. Z. 39 634-8
23. Ismail M E H 2005 Classical and Quantum Orthogonal Polynomials in One Variable (Encyclopedia of Mathematics and its Applications vol 98) (Cambridge: Cambridge University Press)
24. Ismail M E H, Nikonova I and Simeonov P 2004 Difference equations and discriminants for discrete orthogonal polynomials Ramanujan J. 8 475-502
25. Magnus A P 1999 Freud's equations for orthogonal polynomials as discrete Painlevé equations Symmetries and Integrability of Difference Equations (Canterbury, 1996) (London Mathematical Society Lecture Note Series vol 255) (Cambridge: Cambridge University Press) pp 228-43
26. Magnus A P 1995 Painlevé-type differential equations for the recurrence coefficients ofsemi-classical orthogonal polynomials J. Comput. Appl. Math. 57 215-37
27. Maroni P 1987 Prolégomènes à l'étude des polynômes orthogonaux semi-classiques Ann. Mat. Pura Appl. 149 165-84
28. Masuda T 2004 Classical transcendental solutions of the Painlevé equations and their degeneration Tohoku Math. J. 56 457-90
29. Moser J 1975 Finitely Many Mass Points on the Line Under the Influence of an Exponential Potential-An Integrable System (Lecture Notes in Physics vol 38) (Berlin: Springer) pp 469-97
30. Noumi M 2004 Painlevé Equations Through Symmetry (Translations of Mathematical Monographs vol 223) (Providence, RI: American Mathematical Society)
31. V Japan. J. Math. 13 47-76
32. Painlevé P 1900 Mémoire sur les équations différentielles dont l'intégrale générale est uniforme Bull. Soc. Math. Phys. Fr. 28 201-61
33. Painlevé P 1902 Sur les équations différentielles du second ordre et d'ordre supérieure dont l'intégrale générale est uniforme Acta Math. 21 1-85
34. Van Assche W 2007 Discrete Painlevé equations for recurrence coefficients of orthogonal polynomials Difference Equations, Special Functions and Orthogonal Polynomials ed S Elaydi et al (Singapore: World Scientific) pp 687-725
35. Van Assche W and Foupouagnigni M 2003 Analysis of non-linear recurrence relations for the recurrence coefficients of generalized Charlier polynomials J. Nonlinear Math. Phys. 10 231-7