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Constrained orthogonal polynomials

We define sets of orthogonal polynomials satisfying the additional constraint of a vanishing average. These are of interest, for example, for the study of the Hohenberg-Kohn functional for electronic or nucleonic densities and for the study of density fluctuations in centrifuges. We give explicit properties of such polynomial sets, generalizing Laguerre and Legendre polynomials. 
The nature of the dimension 1 subspace completing such sets is described. A numerical example illustrates the use of such polynomials.