On differential polynomials I

Abstract

The content of Part I is nothing else than, the theory of binomial polynomial sequences in infinite variables (u(1),u(2), u(3), . . .) with weight u(l) = l. However, sometimes we are concerned with specialization u(l)→(d/dn)lu, therefore, we call the elements in K[u(1),u(2),u(3), . . .] differential polynomials. As analogies of special polynomials with binomial property, we may construct special differential polynomials with binomial property.