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Confluence et résurgence. (Confluence and resurgence). (French) Zbl 0722.33003

The paper deals with the solutions of the hypergeometric equation in the generic case, where no solutions has logarithmic singularities, e.g., with the following questions: How do the singularities (located at 0, b, \(\infty)\) act on a fundamental system of solutions constructed on a given simply connected domain? What happens as \(b\to \infty\)?

MSC:

33C20 Generalized hypergeometric series, \({}_pF_q\)
32G34 Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation)
32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
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