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arXiv · 1810.01691

The inverse problem for linearly related orthogonal polynomials: General case

A. Peña·M. L. Rezola
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Abstract

We study the inverse problem in the theory of (standard) orthogonal polynomials involving two polynomials families $(P_n)_n$ and $(Q_n)_n$ which are connected by a linear algebraic structure such as $$P_n(x)+\sum_{i=1}^N r_{i,n}P_{n-i}(x)=Q_n(x)+\sum_{i=1}^M s_{i,n}Q_{n-i}(x)$$ for all $n=0,1, \dots$ where $N$ and $M$ are arbitrary nonnegative integer numbers.

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A. Peña, M. L. Rezola. 2018-10-03. The inverse problem for linearly related orthogonal polynomials: General case. https://arxiv.org/abs/1810.01691

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