Special even polynomials and related interpolatory problems

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.

Keywords:

• polynomials
• interpolation
• differential equations
• expansion

AMS Subject Classification :

• 65L05
• 65D05
• 65D15