https://orcid.org/0000-0002-8709-1974
References
- L. Boelen and W. van Assche, Discrete Painlevé equations for recurrence relations of semiclassical Laguerre polynomials, Proc. Amer. Math. Soc. 138 (2010), pp. 1317–1331. doi: 10.1090/S0002-9939-09-10152-1
- A. Bogatskiy, T. Claeys and A. Its, Hankel determinant and orthogonal polynomials for a Gaussian weight with a discontinuity at the edge, Commun. Math. Phys. 347 (2016), pp. 127–162. doi: 10.1007/s00220-016-2691-y
- Y. Chen and M.E.H. Ismail, Jacobi polynomials from compatibility conditions, Proc. Amer. Math. Soc. 133 (2015), pp. 465–472. doi: 10.1090/S0002-9939-04-07566-5
- Y. Chen and M.E.H. Ismail, Ladder operators and differential equations for orthogonal polynomials, J. Phys. A: Math. Gen. 30 (1997), pp. 7818–7829.
- Y. Chen and G. Pruessner, Orthogonal polynomials with discontinuous weights, J. Phys. A: Math. Gen. 38 (2005), pp. L191–L198. doi: 10.1088/0305-4470/38/12/L01
- P.A. Clarkson and K. Jordaan, The relationship between semiclassical Laguerre polynomials and the fourth Painlevé equation, Constr. Approx. 39 (2014), pp. 223–254. doi: 10.1007/s00365-013-9220-4
- G. Filipuk, W. van Assche and L. Zhang, The recurrence coefficients of semi-classical Laguerre polynomials and the fourth Painlevé equation, J. Phys. A: Math. Theor. 45 (2012), p. 205201. doi: 10.1088/1751-8113/45/20/205201
- K. Heun, Zur Theorie der Riemann'schen Functionen zweiter Ordnung mit vier Verzweigungspunkten, (German) Math. Ann. 33(2) (1888), pp. 161–179. doi: 10.1007/BF01443849
- P. Han and Y. Chen, The recurrence coefficients of a semi-classical Laguerre polynomials and the large n asymptotics of the associated Hankel determinant, Random Matrices Theor. Appl. 6 (2017), p. 1740002. doi: 10.1142/S2010326317400020
- T.A. Ishkhanyan and A.M. Ishkhanyan, Solutions of the bi-confluent Heun equations in terms of the Hermite functions, Ann. Phys. 383 (2017), pp. 79–91. doi: 10.1016/j.aop.2017.04.015
- A. Its, Discrete Painlevé equations and orthogonal polynomials, in Symmetries and Integrability of Difference Equations, London mathematical society Lecture Notes Series 381, D. Levi, P. Olver, Z. Thomova and P. Winternitz, eds., Cambridge University Press: Cambridge, 2011, pp. 139–159.
- A. Its and I. krasovsky, Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump, in Integrable Systems and Random Matrices, Contemp. Math. Amer. Math. Soc., Vol. 458, Providence, RI, 2008, pp. 215–248
- C. Min and Y. Chen, Painlevé transcendents and the Hankel determinants generated by a discontinuous Gaussian weight, Math. Methods in Appl. Sci. 42 (2019), pp. 301–321. doi: 10.1002/mma.5347
- A. Ronveaux, Heun's Differential Equations, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1995.
- S.Y. Slavyanov and W. Lay, special Functions. A Unified Theory Based on Singularities, Oxford University Press, Oxford, 2000.
- B.D. Sleeman and V.B. Kuznetsov, Heun Functions, NIST handbook of mathematical functions, 709–721, U.S. Dept. Commerce, Washington, DC, 2010
- M. Zhu and Y. Chen, On properties of a deformed Freud weight, Random Matrices Theor. Appl. 8 (2019), p. 1950004. doi: 10.1142/S2010326319500047