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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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