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Session III.7 - Special Functions and Orthogonal Polynomials

Wednesday, June 21, 17:00 ~ 17:30

About 2-orthogonal polynomial eigenfunctions of a third order differential operator

Teresa A. Mesquita

Instituto Politécnico de Viana do Castelo & Centro de Matemática da Universidade do Porto, Portugal   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The $d$-orthogonal polynomial sequences are known to fulfil certain differential equations of order $d+1$ (e.g. [1, 2, 3]). Considering a generic third order differential operator that does not increase the degree of polynomials, as expressed in [4], we present explicit descriptions of corresponding 2-orthogonal polynomial eigenfunctions. Furthermore, their Hahn-classical character is analysed and other differential identities are given as a consequence of the symbolic approach used in this research work.


[1] K. Douak; The relation of the d-orthogonal polynomials to the Appell polynomials; J. Comput. Appl. Math. 70(2), 279-295 (1996).

[2] K. Douak and P. Maroni; On d-orthogonal Tchebyshev polynomials, I ; Appl. Num. Math., 24, 23-53 (1997).

[3] H. Lima and A. Loureiro; Multiple orthogonal polynomials associated with confluent hypergeometric functions; J. Approx. Theory 260, 36 p. (2020).

[4] T. A. Mesquita and P. Maroni; Around operators not increasing the degree of polynomials; Integral Transforms Spec. Funct. 30, No.5, 383-399 (2019).

[5] T. A. Mesquita; Symbolic Approach to 2-Orthogonal Polynomial Solutions of a Third Order Differential Equation; Math.Comput.Sci. (DOI : 10.1007/s11786-022-00525-8)

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