ON DIFFERENTIAL POLYNOMIALS I

The content of Part I is nothing else than, the theory of binomial pol ynomial sequences in infinite variables (u((1)), u((2)), u((3)),...) w ith weight u((l)) = l. However. sometimes we are concerned with specia lization u((l))-->(d/dn)(l)u, therefore, we call the elements in K[u(( 1)), u((2)), u((3)),...] differential polynomials. As analogies of spe cial polynomials with binomial property, we may construct special diff erential polynomials with binomial property.