|    
[1] Abramowitz M, Stegun I A. Handbook of Mathematical Functions. New York: Dover Publications, 1968 
 
[2] Askey R. Orthogonal Polynomials and Special Functions. Philadelphia, PA: Society for Industrial and 
Applied Mathematics, 1975 
 
[3] Askey R, Ismail M. Recurrence relations, continued fractions and orthogonal polynomials. Memoirs Amer 
Math Soc, 1984, 300 
 
[4] Baik J, Kriecherbauer T, McLaughlin K T -R, Miller P D. Uniform asymptotics for polynomials orthogonal 
with respect to a general class of discrete weights and universality results for associated ensembles. Int 
Math Res Not, 2003, 2003: 821–858 
 
[5] Baik J, Kriecherbauer T, McLaughlin K T -R, Miller P D. Discrete Orthogonal Polynomials. Asymptotics 
and Applications. Annals of Mathematics Studies, 164. Princeton, NJ: Princeton University Press, 2007 
 
[6] Baik J, Suidan T M. Random matrix central limit theorems for nonintersecting random walks. Ann 
Probab, 2007, 35: 1807–1834 
 
[7] Berry M V, Howls C J. Hyperasymptotics for integrals with saddles. Proc R Soc London A, 1991, 434: 
657–675 
 
[8] Bleher P, Its A. Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model. Ann Math, 1999, 150: 185–266 
 
[9] Bleher P, Its A. Double scaling limit in the random matrix model: the Riemann-Hilbert approach. Comm 
Pure Appl Math, 2003, 56: 433–516 
 
[10] Bleistein N. Uniform asymptotic expansions of integrals with many nearby stationary points and algebraic 
singularities. J Math Mech, 1967, 17: 533–559 
 
[11] Borodin A, Olshanski G. Meixner polynomials and random partitions. Mosc Math J, 2006, 6: 629–655 
 
[12] Chan Y, Its A. Painlev´e III and a singular linear statistics in Hermitian random matrix ensembles I. 
preprint 
 
[13] Chester C, Friedman B, Ursell F. An extension of the method of steepest descents. Proc Cambridge Philos 
Soc, 1957, 53: 599–611 
 
[14] Chihara T S. An introduction to orthogonal polynomials. New York, London, Paris: Gordon and Breach 
Science Publishers, 1978 
 
[15] Claeys T, Kuijlaars A B J, Vanlessen M. Multi-critical unitary random matrix ensembles and the general 
Painlev´e II equation. Ann Math, 2008, 168: 601–641 
 
[16] Clancey K, Gohberg I. Factorization of Matrix Functions and Singular Integral Operators. Basel, Boston: 
Birkhäuser, 1981 
 
[17] Costin O, Costin R. Rigorous WKB for finite-order linear recurrence relations with smooth coefficients. 
SIAM J Math Anal, 1996, 27: 110–134 
 
[18] Daems E, Kuijlaars A B J. A Christoffel-Darboux formula for multiple orthogonal polynomials. J Approx 
Theory, 2004, 130: 190–202 
 
[19] Daems E, Kuijlaars A B J. Multiple orthogonal polynomials of mixed type and non-intersecting Brownian 
motions. J Approx Theory, 2007, 146: 91–114 
 
[20] Dai D, Kuijlaars A B J. Painlev´e IV asymptotics for orthogonal polynomials with respect to a modified 
Laguerre weight. to apper in Studies in Applied Mathematics 
 
[21] Dai D, Wong R. Global asymptotics of Krawtchouk polynomials -a Riemann-Hilbert approach. Chin Ann 
Math, Ser B, 2007, 28: 1–34 
 
[22] Dai D, Wong R. Global asymptotics for Laguerre polynomials with large negative parameter-a Riemann- 
Hilbert approach. Ramanujan J, 2008, 16: 181–209 
 
[23] Deift P. Orthogonal polynomials and random matrices: a Riemann-Hilbert approach. Courant Lecture 
Notes 3, New York University, 1999 
 
[24] Deift P. Riemann-Hilbert methods in the theory of orthogonal polynomials//Spectral Theory and Mathematical 
Physics: a Festschrift in Honor of Barry Simon’s 60th Birthday. Proc Sympos Pure Math, 76, Part 2. Providence RI: Amer Math Soc, 2007: 715–740 
 
[25] Deift P. Some open problems in random matrix theory and the theory of integrable systems//Integrable 
Systems and Random Matrices: in Honor of Percy Deift. Contemporary Mathematics 458. Providence RI: Amer Math Soc, 2008 
 
[26] Deift P, Kriecherbauer T, McLaughlin K T -R, Venakides S, Zhou X. Uniform asymptotics for polynomials 
orthogonal with respect to varying exponential weights and applications to universality questions in random 
matrix theory. Comm Pure Appl Math, 1999, 52: 1335–1425 
 
[27] Deift P, Kriecherbauer T, McLaughlin K T -R, Venakides S, Zhou X. Strong asymptotics of orthogonal 
polynomials with respect to exponential weights. Comm Pure Appl Math, 1999, 52: 1491–1552 
 
[28] Deift P, Kriecherbauer T, McLaughlin K T -R, Venakides S, Zhou X. A Riemann-Hilbert approach to 
asymptotic questions for orthogonal polynomials. J Comput Appl Math, 2001, 133: 47–63 
 
[29] Deift P, Zhou X. A steepest descent method for oscillatory Riemann-Hilbert problems, Asymptotics for 
the MKdV equation. Ann Math, 1993, 137: 295–368 
 
[30] Deift P, Zhou X. Asymptotics for the Painleve II equation. Comm Pure Appl Math, 1995, 48: 277–337 
 
[31] Dunkl C F, Xu Y. Orthogonal Polynomials of Several Variables. Cambridge: Cambridge University Press, 
2001 
 
[32] Fokas A S, Its A R, Kitaev A V. The isomonodromy approach to matrix models in 2D quantum gravity. 
Comm Math Phys, 1992, 147: 395–430 
 
[33] Forrester P J, Witte N S. Bi-orthogonal polynomials on the unit circle, regular semi-classical weights and 
integrable systems. Constr Approx, 2006, 24: 201–237 
 
[34] Frenzen C L, Wong R. Uniform asymptotic expansion of Laguerre polynomials. SIAM J Math Anal, 1988, 
19: 1232–1248 
 
[35] Freud G. Orthogonal Polynomials. New York: Pergamon Press, 1971 
 
[36] Geronimus L Y. Orthogonal Polynomials. Vol 108 of Amer Math Soc Transl. Provindence RI: American 
Mathematical Society, 1977 
 
[37] Grosswald E. Bessel Polynomials. Lecture Notes Math 698. New York: Springer, 1978 
 
[38] Ismail M E H. Classical and Quantum Orthogonal Polynomials in One Variable. Cambridge: Cambridge 
University Press, 2005 
 
[39] Jackson D. Fourier Series and Orthogonal Polynomials. Carus Monograph Series, no 6. Mathematical 
Association of America, Oberlin, Ohio, 1941 
 
[40] Johansson K. Discrete orthogonal polynomial ensembles and the Plancherel measure. Ann Math, 2001, 
153: 259–296 
 
[41] Koornwinder T H. Meixner-Pollaczek polynomials and the Heisenberg algebra. J Math Phys, 1989, 30: 
767–769 
 
[42] Kriecherbauer T, McLaughlin K T -R. Strong asymptotics of polynomials orthogonal with respect to Freud 
weights. Int Math Res Not, 1999, 1999: 299–333 
 
[43] Kuijlaars A B J. Riemann-Hilbert analysis for orthogonal polynomials//Koelink E, van Assche W, eds. 
Orthogonal Polynomials and Special Functions: Leuven, 2002. Lecture Notes in Math, 1817. Berlin: Springer, 2003: 167–210 
 
[44] Kuijlaars A B J, Martinez-Finkelshtein A. Strong asymptotics for Jacobi polynomials with varying nonstandard 
parameters. J Anal Math, 2004, 94: 195–234 
 
[45] Kuijlaars A B J, Martinez-Finkelshtein A, Orive R. Orthogonality of Jacobi polynomials with general 
parameters. Electron Trans Numer Anal, 2005, 19: 1–17 (electronic) 
 
[46] Kuijlaars A B J, McLaughlin K T -R. Riemann-Hilbert analysis for Laguerre polynomials with large 
negative parameter. Comput Meth Funct Theory, 2001, 1: 205–233 
 
[47] Kuijlaars A B J, McLaughlin K T -R. Asymptotic zero behavior of Laguerre polynomials with negative 
parameter. Constr Approx, 2004, 20: 497–523 
 
[48] Kuijlaars A B J, McLaughlin K T -R, Van Assche W, Vanlessen M. The Riemann-Hilbert approach to 
strong asymptotics for orthogonal polynomials on  
[−1, 1]. Adv Math, 2004, 188: 337–398 
 
[49] Levenshtein V I. Krawtchouk polynomials and universal bounds for codes and designs in Hamming spaces. 
IEEE Trans Inform Theory, 1995, 41: 1303–1321 
 
[50] Levin E, Lubinsky D S. Orthogonal Polynomials for Exponential Weights. New York: Springer-Verlag, 
2001 
 
[51] Levinson N. Transformation of an analytic function of several variables to a canonical form. Duke Math 
J, 1961, 28: 345–353 
 
[52] Li X, Wong R. On the asymptotics of the Meixner-Pollaczek polynomials and their zeros. Constr Approx, 
2001, 17: 59–90 
 
[53] Lubinsky D S. Asymptotics of orthogonal polynomials: some old, some new, some identities. Acta Appl 
Math, 2000, 61: 207–256 
 
[54] Macdonald I G. Affine Hecke Algebras and Orthogonal Polynomials. Cambridge: Cambridge University 
Press, 2003 
 
[55] Martnez-Finkelshtein A, Martnez-Gonzlez P, Orive R. Zeros of Jacobi polynomials with varying nonclassical 
parameters//Dunkl C, Ismail M, Wong R, eds. Proceedings of the International Workshop on Special Functions. River Edge, NJ: World Scientific, 2000: 98–113 
 
[56] Mastroianni G, Occorsio D. Markov-Sonin Gaussian rule for singular functions. J Comput Appl Math, 
2004, 169: 197–212 
 
[57] Mehta M L. Random Matrices. 2nd ed. Boston: Academic Press, 1991 
 
[58] Mhaskar H N, Saff E B. Extremal problems for polynomials with exponential weights. Trans Amer Math 
Soc, 1984, 285: 203–234 
 
[59] Mnguez Ceniceros J, Van Assche W. Multiple orthogonal polynomials on the unit circle. Constr Approx, 
2008, 28: 173–197 
 
[60] Muskhelishvili N I. Singular Integral Equations. Groningen: Noordhoff, 1953; New York: Reprinted by 
Dover Publications, 1992 
 
[61] Nevai P G. Orthogonal polynomials. Mem Amer Math Soc, 1979, 18(213) 
 
[62] Nevai P G. G´eza Freud, Orthogonal polynomials and Christoffel functions–A case study. J Approx Theory, 
1986, 48(1) 
 
[63] Nikiforov A F, Suslov S K, Uvarov V B. Classical Orthogonal Polynomials of a Discrete Variable. Berlin: 
Springer-Verlag, 1991 
 
[64] Olde Daalhuis A B, Temme N M. Uniform Airy-type expansions of integrals. SIAM J Math, 1994, 25: 304–321 
 
[65] Olver F W J. Asymptotics and Special Functions. New York: Academic Press, 1974 
 
[66] Olver F W J, Lozier D W, Clark C W, Boisvert R F. NIST handbook of mathematical functions. National 
Institute of Standards and Technology, Gaithersberg, Maryland, 2009, (avaliable on the web) 
 
[67] Rakhmanov E A. Asymptotic properties of orthogonal polynomials on the real axis (Russian). Mat Sb 
(N.S.), 1982, 119(161): 163–203, 303; English translation in Math USSR-Sb, 1984, 47: 155–193 
 
[68] Simon B. Orthogonal polynomials on the unit circle, Part 1. Providence RI: American Mathematical 
Society, 2005 
 
[69] Simon B. Orthogonal polynomials on the unit circle, Part 2. Providence RI: American Mathematical 
Society, 2005 
 
[70] Stahl H, Totik V. General Orthogonal Polynomials. Cambridge: Cambridge University Press, 1992 
 
[71] Szegö G. Orthogonal polynomials. Fourth edition. Colloquium Publications Vol 23. Providence RI: Amer 
Math Soc, 1975 
 
[72] Totik V. Orthogonal polynomials. Surv Approx Theory, 2005, 1: 70–125 
 
[73] Van Assche W. Asymptotics for Orthogonal Polynomials. Lect Notes Math 1265. Berlin: Springer-Verlag, 
1987 
 
[74] Van Assche W, Geronimo J S, Kuijlaars A B J. Riemann-Hilbert problems for multiple orthogonal polynomials//Bustoz J, et al. eds. NATO ASI Special Functions 2000. Dordrecht: Kluwer Academic Publishers, 
2001: 23–59 
 
[75] Wang Z, Wong R. Asymptotic expansions for second-order linear difference equations with a turning point. 
Numer Math, 2003, 94: 147–194 
 
[76] Wang Z, Wong R. Linear difference equations with transition points. Math Comp, 2005, 74: 629–653 
 
[77] Wang Z, Wong R. Bessel-type asymptotic expansions via the Riemann-Hilbert approach. Proc R Soc Lond 
Ser A, 2005, 461: 2839–2856 
 
[78] Wang Z,Wong R. Uniform asymptotics for orthogonal polynomials with exponential weights -the Riemann- 
Hilbert approach. Stud Appl Math, 2005, 115: 139–155 
 
[79] Wang Z, Wong R. Uniform asymptotics of the Stieltjes-Wigert polynomials via the Riemann-Hilbert approach. 
J Math Pures Appl, 2006, 85: 698–718 
 
[80] Wong R. Asymptotics Approximations of Integrals. Boston: Academic Press, 1989 
 
[81] Wong R. Orthogonal polynomials and their asymptotic behavior//Special Functions (Hong Kong, 1999). 
River Edge, NJ: World Scientific Publishing, 2000: 409–422 
 
[82] Wong R, Li H. Asymptotic expansions for second-order linear difference equations. J Comput Appl Math, 
1992, 41: 65–94 
 
[83] Wong R, Li H. Asymptotic expansions for second-order linear difference equations II. Studies Appl Math, 
1992, 87: 289–324 
 
[84] Wong R, Zhang L. Global asymptotics of Hermite polynomials via Riemann-Hilbert approach. Discrete 
Contin Dyn Syst Ser B, 2007, 7: 661–682 
 
[85] Wong R, Zhang W -J. Uniform asymptotics for Jacobi polynomials with varying large negative parameters 
-a Riemann-Hilbert approach. Trans Amer Math Soc, 2006, 358: 2663–2694 
 
[86] Wong R, Zhao Y -Q. On a uniform treatment of Darboux’s method. Constr Approx, 2005, 21: 225–255 
 
[87] Xu S -X, Zhao Y -Q. Resurgence relation and global asymptotic analysis of orthogonal polynomials via 
the Riemann-Hilbert approach. preprint 
 
[88] Zhao Y -Q. Uniform asymptotics for orthogonal polynomials via the Riemann-Hilbert approach. Appl 
Anal, 2006, 85: 1165–1176 
 
[89] Zhou J -R, Zhao Y -Q. Uniform asymptotics of the Pollaczek polynomials via the Riemann-Hilbert approach. 
Proc R Soc A, 2008, 464: 2091–2112
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