참고문헌
- A. Angelesco, Sur l'approximation simultanee de plusieurs integrales definies, C. R. Paris, 167 (1918), 629-631.
- A. I. Aptekarev, Multiple orthogonal polynomials, J. Comput. Appl. Math. 99 (1998), no. 1-2, 423-447. https://doi.org/10.1016/S0377-0427(98)00175-7
- A. I. Aptekarev, A. Branquinho, and W. Van Assche, Multiple orthogonal polynomials for classical weights, Trans. Amer. Math. Soc. 355 (2003), no. 10, 3887-3914. https://doi.org/10.1090/S0002-9947-03-03330-0
- A. I. Aptekarev, V. Kalyagin, G. Lopez Lagomasino, and I. A. Rocha, On the limit behavior of recurrence coefficients for multiple orthogonal polynomials, J. Approx. Theory 139 (2006), no. 1-2, 346-370. https://doi.org/10.1016/j.jat.2005.09.011
- B. Beckermann, J. Coussement, andW. Van Assche, Multiple Wilson and Jacobi-Pineiro polynomials, J. Approx. Theory 132 (2005), no. 2, 155-181. https://doi.org/10.1016/j.jat.2004.12.001
- P. M. Bleher and A. B. J. Kuijlaars, Large n limit of Gaussian random matrices with external source. I, Comm. Math. Phys. 252 (2004), no. 1-3, 43-76. https://doi.org/10.1007/s00220-004-1196-2
- P. M. Bleher and A. B. J. Kuijlaars, Integral representations for multiple Hermite and multiple Laguerre polynomials, Ann. Inst. Fourier (Grenoble) 55 (2005), no. 6, 2001-2014. https://doi.org/10.5802/aif.2148
- T. S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, 1978.
-
P. Desrosiers, Duality in random matrix ensembles for all
${\beta}$ , Nuclear Phys. B 817 (2009), no. 3, 224-251. https://doi.org/10.1016/j.nuclphysb.2009.02.019 - P. Desrosiers and P. J. Forrester, Asymptotic correlations for Gaussian and Wishart matrices with external source, Int. Math. Res. Not. (2006), Art. ID 27395, 43p.
- P. Desrosiers and P. J. Forrester, A note on biorthogonal ensembles, J. Approx. Theory 152 (2008), no. 2, 167-187. https://doi.org/10.1016/j.jat.2007.08.006
- M. E. H. Ismail, Classical and Quantum Orthogonal Polynomials in One Variable, in Encyclopedia of Mathematics and its Applications, vol. 98, Cambridge University Press, 2005.
- D. W. Lee, Properties of multiple Hermite and multiple Laguerre polynomials by the generating function, Integral Transforms Spec. Funct. 18 (2007), no. 11-12, 855-869. https://doi.org/10.1080/10652460701510725
- D. W. Lee, Generating functions and multiple orthogonal polynomials, In 5th Asian Mathematical Conference Proceedings, Vol. II, (Yahya Abu Hasan et al., ed.), 44-51, 2009.
- V. Lysov and F. Wielonsky, Strong asymptotics for multiple Laguerre polynomials, Constr. Approx. 28 (2008), no. 1, 61-111. https://doi.org/10.1007/s00365-006-0648-1
- E. M. Nikishin and V. N. Sorokin, Rational Approximations and Orthogonality, Translations of Mathematical Monographs, 92. American Mathematical Society, Providence, RI, 1991.
- E. D. Rainville, Special Functions, Chelsea Publishing Company, New York, 1960.
- G. Szego, Orthogonal Polynomials, Amer. Math. Soc. Coll. Publ. vol 23., 4th ed., Amer. Math. Soc., Providence, RI, 1975.
- W. Van Assche, Multiple orthogonal polynomials, irrationality and transcendence, Continued fractions: from analytic number theory to constructive approximation (Columbia, MO, 1998), 325-342, Contemp. Math., 236, Amer. Math. Soc., Providence, RI, 1999.
- W. Van Assche, Nearest neighbor recurrence relations for multiple orthogonal polynomials, J. Approx. Theory 163 (2011), no. 10, 1427-1448. https://doi.org/10.1016/j.jat.2011.05.003
- W. Van Assche and E. Coussement, Some classical multiple orthogonal polynomials, J. Comput. Appl. Math. 127 (2001), no. 1-2, 317-347. https://doi.org/10.1016/S0377-0427(00)00503-3