On \(d\)-orthogonal Tchebychev polynomials. I (Q1360526)

The authors investigate the problem of obtaining all the \(d\)-orthogonal sequences \(\{P_n\}_{n\geq 0}\) which satisfy \(P_n^{(1)}= P_n\) where \(P_n\), \(n=0,1,\dots\), are the associated polynomials of \(\{P_n\}\). The resulting polynomials turn out to be natural extensions of Chebyshev monic polynomials of the second kind. The particular case \(d=2\) of these polynomials has been studied in detail from the viewpoint of their differential equation, recurrence coefficients and generating functions.