References
- W.H. Abdi, On {\it q}-Laplace transforms, Proc. Nat. Acad. Sci. India Sect. A. 29 (1960), pp. 389–408.
- W.H. Abdi, Certain inversion and representation formulae for {\it q}-Laplace transforms, Math. Z. 83 (1964), pp. 238–249.
- W. Balser, From Divergent Power Series to Analytic Functions, Theory and Application of Multisummable Power Series Vol. 1582, Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1994.
- V. Bugeaud, Groupe de Galois local des équations aux {\it q}-différences irrégulières, PhD thesis, Institut de Mathématiques de Toulouse, 2012.
- T. Dreyfus, Building meromorphic solutions of {\it q}-difference equations using a Borel--Laplace summation, Int. Math. Res. Not. IMRN (15) (2015), pp. 6562–6587.
- T. Dreyfus, Confluence of meromorphic solutions of {\it q}-difference equations, Ann. Inst. Fourier (Grenoble) 65(2) (2015), pp. 431–507.
- L. Di Vizio, J.-P. Ramis, J. Sauloy, and C. Zhang, Équations aux q-différences, Gaz. Math. (96) (2003), pp. 20–49.
- L. Di Vizio and C. Zhang, On {\it q}-summation and confluence, Ann. Inst. Fourier (Grenoble) 59(1) (2009), pp. 347–392.
- W. Hahn, Beiträge zur Theorie der Heineschen Reihen. Die 24 Integrale der Hypergeometrischen {\it q}-Differenzengleichung. Das {\it q}--Analogon der Laplace-Transformation, Math. Nachr. 2 (1949), pp. 340–379.
- B. Malgrange, Sommation des séries divergentes. Exposition. Math. 13(2–3) (1995), pp. 163–222.
- F. Marotte and C. Zhang, Multisommabilité des séries entières solutions formelles d’une équation aux {\it q}-différences linéaire analytique, Ann. Inst. Fourier (Grenoble) 50(6) (2000/2001), pp. 1859–1890.
- C. Praagman, Fundamental solutions for meromorphic linear difference equations in the complex plane, and related problems, J. Reine Angew. Math. 369 (1986), pp. 101–109.
- J.-P. Ramis, Phénomène de Stokes et filtration Gevrey sur le groupe de Picard--Vessiot, C. R. Acad. Sci. Paris Sér. I Math.. 301(5) (1985), pp. 165–167.
- J.-P. Ramis, About the growth of entire functions solutions of linear algebraic {\it q}-difference equations, Ann. Fac. Sci. Toulouse Math. (6). 1(1) (1992), pp. 53–94.
- J.-P. Ramis and J. Sauloy, The {\it q}-analogue of the wild fundamental group. I, Algebraic, analytic and geometric aspects of complex differential equations and their deformations. Painlevé hierarchies, RIMS Kôkyûroku Bessatsu, B2, Research Institute for Mathematical Sciences (RIMS), Kyoto, 2007, pp. 167–193.
- J.-P. Ramis and J. Sauloy, The {\it q}-analogue of the wild fundamental group. II, Astérisque 323 (2009), pp. 301–324.
- J.-P. Ramis, J. Sauloy, and C. Zhang, Local analytic classification of {\it q}-difference equations, Astérisque. 355 (2013), pp. vi+151.
- J.-P. Ramis and C. Zhang, Développement asymptotique {\it q}-Gevrey et fonction thêta de Jacobi, C. R. Math. Acad. Sci. Paris 335(11) (2002), pp. 899–902.
- J. Sauloy, Systèmes aux {\it q}-différences singuliers réguliers: Classification, matrice de connexion et monodromie, Ann. Inst. Fourier (Grenoble) 50(4) (2000), pp. 1021–1071.
- H. Tahara, q-analogues of laplace and borel transforms by means of q-exponentials, Preprint (2014).
- M. van der Put and M. Reversat, Galois theory of {\it q}-difference equations, Ann. Fac. Sci. Toulouse Math. (6). 16(3) (2007), pp. 665–718.
- M. van der Put and M.F. Singer, Galois theory of linear differential equations, Vol. 328, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin, 2003.
- C. Zhang, Développements asymptotiques {\it q}-Gevrey et séries {\it Gq}-sommables, Ann. Inst. Fourier (Grenoble). 49(1): vi-vii, x (1999), pp. 227–261.
- C. Zhang, Transformations de {\it q}-Borel--Laplace au moyen de la fonction thêta de Jacobi, C. R. Acad. Sci. Paris Sér. I Math.. 331(1) (2000), pp. 31–34.
- C. Zhang, Sur la fonction {\it q}-gamma de Jackson, Aequationes Math. 62(1–2) (2001), pp. 60–78.
- C. Zhang, Une sommation discrète pour des équations aux {\it q}-différences linéaires et à coefficients analytiques: théorie générale et exemples, Differential equations and the Stokes phenomenon, World Scientific Publishing, River Edge, NJ, 2002, pp. 309–329.
- C. Zhang, Sur les fonctions {\it q}-Bessel de Jackson, J. Approx. Theory 122(2) (2003), pp. 208–223.