Abstract
The large-order behaviour of power series used in quantum theory (perturbation series and the operator-product expansion) is discussed and relevant summation methods are reviewed. It is emphasised that, in most physically interesting situations, the mere knowledge of the expansion coefficients is not sufficient for a unique determination of the function expanded, and the necessity of some additional, extra-perturbative, input is pointed out. Several possible nonperturbative inputs are suggested. Applications to various problems of quantum chromodynamics are considered.This lecture was presented on the special Memorial Day dedicated to Professor Ryszard Ra̧czka at this Workshop. The last section is devoted to my personal recollections of this remarkable personality.
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