## $$q$$-factorial series, $$q$$-difference operators and confluence. (Séries de $$q$$-factorielles, opérateurs aux $$q$$-différences et confluence.)(French. English summary)Zbl 1096.33009

Summary: We study some properties of $$q$$-factorial and allied series and show how by confluence they give rise to usual factorial series. We apply this mechanism to the study of difference systems regular at infinity viewed as limits of $$q$$-difference systems.

### MSC:

 33D15 Basic hypergeometric functions in one variable, $${}_r\phi_s$$ 39A10 Additive difference equations 34M30 Asymptotics and summation methods for ordinary differential equations in the complex domain 39A13 Difference equations, scaling ($$q$$-differences)
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### References:

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