Abstract
(1) f(uv, (UV)', * * * X (UV) (n)) = f(U, U, . I n(8)) + f(v,V, V n)) for arbitrary x and arbitrary nonzero n times differentiable functions u(x), v(x). What is the form of f for general n? At the suggestion of R. Bellman and of N. J. Fine (who has given another solution of this problem),' we give here a solution which seems to stress the proper setting of the problem. Set u=e8, v=et; then we can write
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