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$$q$$-Borel-Laplace transforms by means of the Jacobi theta function. (Transformations de $$q$$-Borel-Laplace au moyen de la fonction thêta de Jacobi.) (French) Zbl 1101.33307
Summary: In this paper, we present a notion of asymptotic expansion adapted for $$q$$-Gevrey power series of order one. It is shown that this notion is naturally related to the Jacobi theta function, which is a $$q$$-analog of the usual exponential function. A summation method is then obtained.

##### MSC:
 33D15 Basic hypergeometric functions in one variable, $${}_r\phi_s$$ 44A10 Laplace transform
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