A formula for summing divergent series
نویسندگان
چکیده
منابع مشابه
Variational perturbation theory for summing divergent tunnelling amplitudes
We present a method for evaluating divergent series with factorially growing coefficients of equal sign. The method is based on an analytic continuation of variational perturbation theory from the regime of alternating signs. We demonstrate its power first by applying it to the exactly known partition function of the anharmonic oscillator in zero space–time dimensions (the simple integral). The...
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We give a natural extension of the classical definition of Césaro convergence of a divergent sequence/function. This involves understanding the spectrum of eigenvalues and eigenvectors of a certain Césaro operator on a suitable space of functions or sequences. The essential idea is applicable in identical fashion to other summation methods such as Borel’s. As an example we show how to obtain th...
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ژورنال
عنوان ژورنال: The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
سال: 1975
ISSN: 0334-2700,1839-4078
DOI: 10.1017/s0334270000001089