That means where . In this context the solution of a special Goursat problem of the homogeneous equation is very important. It should be remarked, that the solution of the Goursat problem depends holomorphicaly on w . Now let us define the Goursat conditions. By recursion the Goursat conditions of k are known.
Some abbreviations are useful.
Let if and all the other indices are zero. Let us denote all those indices, which are zero, by and all the other indices, which are one by . That means, the function depends only the variables . By complete induction. There are no more difficulties for the reader to complete the proof.