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The class of polynomials L k (x), k=1, 2, …, of degree 2k+1 satisfying the differential equation L″ k (x)=L k−1(x) and the initial condition L k (0)=0 is introduced. For any choice of one more condition, we have a definite and special sequence of polynomials. The sequences of polynomials related to a linear functional F on C 2k+1 are interesting, since they are the basis of a particular non-classic interpolatory problem.
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Costabile et al. (2009) studied this question.
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