Recurrence relation and multi-indexed polynomials of the second kind
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Exceptional orthogonal polynomials fulfil recurrence relations with constant, and with variable dependent coefficients. Considering the second type relations we can define multi-indexed polynomials of the second kind. In some cases they are also exceptional orthogonal polynomials. The other types of multi-indexed polynomials of the second kind are investigated in case of 2-step Darboux transform.
Key words and phrasesexceptional orthogonal polynomial recurrence relation Darboux transform
Mathematics Subject Classification33C47 33C45
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- 1.T. S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach (New York, 1978)Google Scholar
- 2.P. A. Clarkson, D. Gómez-Ullate, Y. Grandati, and R. Milson, Rational solutions of higher order Painlevé systems. I, arXiv:1811.09274 (2018)
- 4.R. H. Fowler, Some results on the form near infinity of real continuous solutions of a certain type of second order differential equation, Proc. London Math. Soc., (1914), 341–371Google Scholar
- 5.M. Á. García-Ferrero, D. Gómez-Ullate and R. Milson, A Bochner type classification theorem for exceptional orthogonal polynomials, J. Math. Anal. Appl. (to appear), arXiv:1603.04358
- 10.D. Gómez-Ullate, N. Kamran,and R. Milson, On orthogonal polynomials spanning a non-standard flag, in: Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, Contemp. Math., 563, Amer. Math. Soc. (Providence, RI, 2012), pp. 51–72Google Scholar
- 14.C. Liaw, L. L. Littlejohn, R. Milson, and J. Stewart, A new class of exceptional orthogonal polynomials: the type III Xm-Laguerre polynomials and the spectral analysis of three types of exceptional Laguerre polynomials, arXiv:1407.4145 (2014)
- 17.S. Odake, Recurrence relations of the multi-indexed orthogonal polynomials. II, J. Math. Phys., 56 (2015), 053506Google Scholar
- 18.S. Odake, Recurrence relations of the multi-indexed orthogonal polynomials. III, J. Math. Phys., 57 (2016), 023514Google Scholar
- 19.S. Odake, Recurrence relations of the multi-indexed orthogonal polynomials. IV: closure relations and creation/annihilation operators, J. Math. Phys. 57 (2016), 113503Google Scholar
- 24.G. Szegő, Orthogonal Polynomials, AMS Coll. Publ., Vol. XXXIII, Amer. Math. Soc. (New York, 1959)Google Scholar