(N is the set of non-negative integers). Another theorems is a result of the same type for ||e-x-\frac{p(x)}{q(x)}||L_{oo[0,1]}, with the restriction on p(x) that its coefficients are non-negative. It should have been mentioned that the rational function rm,n(x) with denominator of degree m and numerator of degree n (not m), both defined by an integral, for which it is shown that, theorem 2,
is in fact the Padé approximant of e-x. From the various results applied during the proofs of the eight theorems we mention Lagrange's interpolation theorem, interpolation polynomials from the calculus of differences and a lemma of the second author which says that [p(x)] 1/n is concave on [a,b] when the polynomial p has degree at most n, has only real zeros and p(x) < 0 on [a,b].
Reviewer: H.Jager
Classif.: * 41A20 Approximation by rational functions
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