Special even polynomials and related interpolatory problems.

A class of polynomials Lk(x), k=1, 2, ... of degree 2k satisfying the differential equation L''k(x)=Lk-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. [ABSTRACT FROM AUTHOR]