Let us come back to the problem which was considered in § 1.4.1 and solved by Hermite (Proposition 1.20): Given two integers n0 ≥ 0, n1 ≥ 0, find two polynomials A and B with A of degree ≤ n0 and B of degree ≤ n1 such that the function R(z) = B(z)e −A(z) has a zero at the origin of multiplicity ≥ N + 1 with N = n0 + n1. From § 1.4.3 one easily deduces that there is a non-trivial solution, and i...