On the positive powers of q-analogs of Euler series
Abstract
The most simple and famous divergent power series coming from ODE may be the so-called Euler series Σn 0(-1)n\,n!\,xn+1, that, as well as all its positive powers, is Borel-summable in any direction excepted the negative real half-axis. By considering a family of linear q-difference operators associated with a given first order non-homogenous q-difference equation, it will be shown that the summability order of q-analoguous counterparties of Euler series depends upon of the degree of power under consideration.
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