Strong asymptotics for jacobi polynomials with varying nonstandard parameters

Journal d'Analyse Mathematique

Volumn 94, Issue , 2004, Pages 195-234

  Kuijlaars, A B J ^a   Martinez Finkelshtein A ^b,c  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b UNIVERSITY OF ALMERÍA   (Spain)

^c UNIVERSITY OF GRANADA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 14644436366     PISSN: 00217670     EISSN: 15658538     Source Type: Journal    
DOI: 10.1007/BF02789047     Document Type: Article

References (34)

1. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover Publications, New York, 1968.
2. A. I. Aptekarev, Sharp constants for rational approximations of analytic functions, Sb. Math. 193 (2002), no. 1-2, 1-72.
3. J. Baik, P. Deift, K. T.-R. McLaughlin, P. Miller and X. Zhou, Optimal tail estimates for directed last passage site percolation with geometric random variables, Adv. Theor. Math. Phys. 5 (2001), 1207-1250.
4. C. Bosbach and W. Gawronski, Strong asymptotics for Jacobi polynomials with varying weights, Methods Appl. Anal. 6 (1999), 39-54.
5. L.-C. Chen and M. E. H. Ismail, On asymptotics of Jacobi polynomials, SIAM J. Math. Anal. 22 (1991), 1442-1449.
6. P. A. Deift, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, New York University Courant Institute of Mathematical Sciences, New York, 1999.
7. P. Deift, T. Kriecherbauer, K. T.-R. McLaughlin, S. Venakides and X. Zhou, Strong asymptotics of orthogonal polynomials with respect to exponential weights, Comm. Pure Appl. Math. 52 (1999), 1491-1552.
8. P. Deift, T. Kriecherbauer, K. T.-R. McLaughlin, S. Venakides and X. Zhou, Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory, Comm. Pure Appl. Math. 52 (1999), 1335-1425.
9. P. Deift and X. Zhou, A steepest descent method for oscillatory Riemann-Hilbert problems: asymptotics for the MKdV equation, Ann. of Math. (2) 137 (1993), 295-368.
10. H. Dette and W. J. Studden, Some new asymptotic properties for the zeros of Jacobi, Laguerre, and Hermite polynomials, Constr. Approx. 11 (1995), 227-238.
11. K. Driver and P. Duren, Asymptotic zero distribution of hypergeometric polynomials, Numer. Algorithms 21 (1999), 147-156.
12. K. Driver and P. Duren, Trajectories of the zeros of hypergeometric polynomials F(-n, b; 2b; z) for b < - 1/2, Constr. Approx. 17 (2001), 169-179.
13. K. Driver and M. Möller, Zeros of hypergeometric polynomials F(-n, b; -2n; z), J. Approx. Theory 110 (2001), 74-87.
14. P. Duren and K. Boggs, Zeros of hypergeometric functions, Comput. Methods Funct. Theory 1 (2001), 275-287.
15. P. Duren and B. J. Guillou, Asymptotic properties of zeros of hypergeometric polynomial, J. Approx. Theory 111 (2001), 329-343.
16. A. Fokas, A. Its and A. Kitaev, The isomonodromy approach to matrix models in 2D quantum gravity, Comm. Math. Phys. 147 (1992), 395-430.
17. (an+α, bn+β), in Progress in Approximation Theory (P. Nevai and A. Pinkus, eds.), Academic Press, New York, 1991, pp. 379-404.
18. A. A. Gonchar and E. A. Rakhmanov, Equilibrium distributions and rate of the rational approximation of analytic functions, Mat. USSR Sbornik 62 (1989), 305-348; translation from Mat. Sb., Nov. Ser. 134(176), No. 3 (11) (1987), 306-352.
19. A. A. Gonchar and E. A. Rakhmanov, Equilibrium distributions and rate of the rational approximation of analytic functions, Mat. USSR Sbornik 62 (1989), 305-348; translation from Mat. Sb., Nov. Ser. 134(176), No. 3 (11) (1987), 306-352.
20. S. Kamvissis, K. T.-R. McLaughlin and P. D. Miller, Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation, Annals of Mathematics Studies 154, Princeton University Press, Princeton, 2003.
21. A. B. J. Kuijlaars, A. Martínez-Finkelshtein and R. Orive, Orthogonality of Jacobi polynomials with general parameters. Electron. Trans. Numer. Anal., to appear; preprint math.CA/0301037.
22. A. B. J. Kuijlaars and K. T.-R. McLaughlin, Asymptotic zero behavior of Laguerre polynomials with negative parameter, Constr. Approx. 20 (2004), 497-523.
23. A. B. J. Kuijlaars and K. T.-R. McLaughlin, Riemann-Hilbert analysis for Laguerre polynomials with large negative parameter, Comput. Methods Funct. Theory 1 (2001), 205-233.
24. A. B. J. Kuijlaars and W. Van Assche, The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients, J. Approx. Theory 99 (1999), 167-197.
25. A. B. J. Kuijlaars, W. Van Assche and F. Wielonsky, Quadratic Hermite-Padé approximation to the exponential function: a Riemann-Hilbert approach, Constr. Approx., to appear; preprint math.CA/0302357.
26. A. Martínez-Finkelshtein, P. Martínez-González and R. Orive, Zeros of Jacobi polynomials with varying non-classical parameters, in Special Functions (Hong Kong, 1999), World Sci. Publishing, River Edge, NJ, 2000, pp. 98-113.
27. (αn, βn) (x), Trans. Amer. Math. Soc. 249(1979), 159-162.
28. F. W. J. Olver, Asymptotics and Special Functions, Academic Press, Boston, 1974.
29. C. Pommerenke, Univalent Functions, Vandenhoeck & Ruprecht, Göttingen, 1975.
30. E. B. Saff and V. Totik, Logarithmic Potentials with External Fields, Springer-Verlag, Berlin, 1997.
31. H. Stahl, Orthogonal polynomials with complex-valued weight function. I, II, Constr. Approx. 2 (1986), 225-240, 241-251.
32. K. Strebel, Quadratic Differentials, Springer-Verlag, Berlin, 1984.
33. G. Szegö, Orthogonal Polynomials, fourth ed., Amer. Math. Soc., Providence, RI, 1975.
34. N. M. Temme, Large parameter cases of the Gauss hypergeometric function, J. Comput. Appl. Math. 153 (2003), 441-462.