Korean J. Math.  Vol 25, No 2 (2017)  pp.181-199
DOI: https://doi.org/10.11568/kjm.2017.25.2.181

The recurrence coefficients of the orthogonal polynomials with the weights $w_\alpha(x)= x^\alpha \exp(-x^3+tx)$ and $W_\alpha(x)=|x|^{2\alpha+1} \exp(-x^6+tx^2)$

Haewon Joung


In this paper we consider the orthogonal polynomials with weights  $w_\alpha(x)= x^\alpha \exp(-x^3+tx)$ and $W_\alpha(x)=|x|^{2\alpha+1} \exp(-x^6+tx^2)$. Using the compatibility conditions for the ladder operators for these orthogonal polynomials, we derive several difference equations satisfied by the recurrence coefficients of these orthogonal polynomials. We also derive differential-difference equations and second order linear ordinary differential equations satisfied by these orthogonal polynomials.


Orthogonal polynomials, Recurrence coefficients, Ladder operators.

Subject classification

42C05, 39A10


Full Text:



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