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Voros coefficients at the origin and at the infinity of the generalized hypergeometric differential equations with a large parameter. (English) Zbl 1510.34192

Voros coefficients have been introduced mainly for second-order ordinary differential equations and used effectively in the study of their turning points, of the description of parametric Stokes phenomena, of calculation of monodromies and of the relations between Borel resummed WKB solutions and classical special functions. The authors consider Voros coefficients of generalized hypergeometric differential equations with a large parameter. Their explicit forms are given for the origin and for infinity. It is shown that they are Borel summable in some specified regions in the space of parameters and their Borel sums in the regions are given.

MSC:

34M60 Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent)
33C20 Generalized hypergeometric series, \({}_pF_q\)
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
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