## Multisummability of formal power series solutions of linear analytic $$q$$-difference equations. (Multisommabilité des séries entières solutions formelles d’une équation aux $$q$$-différences linéaire analytique.)(French)Zbl 1063.39001

Summary: We introduce a $$q$$-analogous version of the elementary acceleration method of Écalle-Martinet-Ramis and define the $$Gq$$-multisummable power series. We show that every formal power series satisfying a linear analytic $$q$$-difference equation is $$Gq$$-multisummable.

### MSC:

 39A10 Additive difference equations 40G99 Special methods of summability
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### References:

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