Abstract
Sufficient conditions for the (real) analyticity of an infinitely differentiable function ƒ(x) are deduced using sequences of polynomial (differential) operators. This generalizes the concept of an absolutely monotonic function. The primary method uses the connection coefficients between pairs of sequences of polynomials, {( x + cn) n } and { P n ( x)}, for n ⩾ 0, where c is a constant and { P n ( x)} is in some general class.
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