An algebraic approach to Lidstone polynomials

A new definition of Lidstone polynomials [G.L. Lidstone, Note on the extension of Aitken’s theorem (for polynomial interpolation) to the Everett types, Proc. Edinb. Math. Soc. 2 (2) (1929) 16–19] is proposed; this is a Hessemberg determinantal form. The algebraic approach provides an elementary proof of the main recursive properties of Lidstone polynomials.