Abstract
The regularity of a linear combination of r consecutive elements of a monic d-orthogonal polynomial sequence has been studied when $$(r-1)$$ is a multiple of d. This problem can be solved without the introduction of the concept of d-quasi-orthogonality. In the present contribution, we deal with the problem of d-orthogonality of a linear combination of two elements of a monic d-orthogonal polynomial sequence. This problem is also equivalent to the study the regularity of the left product of a linear form by a matrix polynomial of degree one.
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