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Abstract
A class of polynomials L k (x), k=1, 2, … of degree 2k satisfying the differential equation L″ k (x)=L k−1(x) and the initial condition L′ k (0)=0 is introduced. A relationship with a particular sequence of Appell polynomials of even degree is given. For any choice of one more boundary condition, a special sequence of polynomials is obtained. Special sequences of these polynomials are the basis of an interpolatory problem related to a fixed linear functional. Some of these polynomials are well known in literature. Finally, the problem of the polynomial expansion in these basis of real C ∞ functions is posed. Some examples are given.