Painlevé VI and Hankel determinants for the generalized Jacobi weight

Journal of Physics A: Mathematical and Theoretical

Volumn 43, Issue 5, 2010, Pages

  Dai, D ^a   Zhang, L ^b  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 76749100356     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/43/5/055207     Document Type: Article

References (26)

1. Abramowitz M and Stegun I A 1992 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (reprint of the 1972 edition) (New York: Dover)
2. Basor E and Chen Y 2009 Painlevé V and the distribution function of a discontinuous linear statistics 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. m), m an even positive integer J. Approx. Theory 46 408-10
5. Bonan S, Lubinsky D S and Nevai P 1987 Orthogonal polynomials and their derivatives: II SIAM J. Math. Anal. 18 1163-76
6. Bonan S and Nevai P 1984 Orthogonal polynomials and their derivatives: I J. Approx. Theory 40 134-47
7. Borodin A and Deift P 2002 Fredholm determinants, Jimbo-Miwa-Ueno τ-functions, and representation theory Comm. Pure Appl. Math. 55 1160-230
8. Chen Y and Dai D 2008 Painlevé V and a Pollaczek-Jacobi type orthogonal polynomials arXiv:0809.3641
9. Chen Y and Feigin M V 2006 Painlevé IV and degenerate Gaussian unitary ensembles J. Phys. A: Math. Gen. 39 12381-93
10. Chen Y and Ismail M 1997 Ladder operators and differential equations for orthogonal polynomials J. Phys. A: Math. Gen. 30 7817-29 (Pubitemid 127375455)
11. Chen Y and Ismail M 2005 Jacobi polynomials from compatibility conditions Proc. Am. Math. Soc. 133 465-72
12. Chen Y and Its A R 2010 Painlevé III and a singular linear statistics in Hermitian random matrix ensembles: I J. Approx. Theory at press (doi:10.1016/j.jat.2009.05.005)
13. Forrester P J and Witte N S 2006 Random matrix theory and the sixth Painlevé equation J. Phys. A: Math. Gen. 39 12211-33
14. Foulquie Moreno A, Martinez-Finkelshtein A and Sousa V L 2009 On a conjecture of A Magnus concerning the asymptotic behavior of the recurrence coefficients of the generalized Jacobi polynomials arXiv:0905.2753
15. Gammel J L and Nuttall J 1982 Note on generalized Jacobi polynomials The Riemann Problem, Complete Integrability and Arithmetic Applications (Bures-sur-Yvette/New York, 1979/1980) (Lecture Notes in Math., vol 925) (Berlin: Springer) pp 258-70
16. Haine L and Semengue J 1999 The Jacobi polynomial ensemble and the Painlevé VI equation J. Math. Phys. 40 2117-34
17. 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)
18. Jimbo M and Miwa T 1981 Monodromy perserving deformation of linear ordinary differential equations with rational coefficients: II Physica D 2 407-48
19. Magnus A P 1995 Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials J. Comput. Appl. Math. 57 215-37
20. Mehta M L 2004 Random Matrices 3rd edn (New York: Elsevier)
21. Nevai P, Erdélyi T and Magnus A P 1994 Generalized Jacobi weights, Christoffel functions, and Jacobi polynomials SIAM J. Math. Anal. 25 602-14
22. Okamoto K 1981 On the τ-function of the Painlevé equations Physica D 2 525-35
23. Shohat J 1939 A differential equation for orthogonal polynomials Duke Math. J. 5 401-17
24. Szeg G 1975 Orthogonal Polynomials (AMS Colloquium Publications, vol 23) 4th edn (Providence, RI: American Mathematical Society)
25. Vanlessen M 2003 Strong asymptotics of the recurrence coefficients of orthogonal polynomials associated to the generalized Jacobi weight J. Approx. Theory 125 198-237
26. Vértesi P 1999 Uniform asymptotics of derivatives of orthogonal polynomials based on generalized Jacobi weights Acta Math. Hung. 85 97-130