Changgui Zhang

Sur les fonctions q -Bessel de Jackson

(About Jackson q-Bessel functions)Laplace transform allows to resolve differential equations in the neighborhood of an irregular singular point. The purpose of the article is to study how to apply a basic Borel-Laplace transformation to q-difference equations satisfied by the q-Bessel functions of F.H. Jackson. Connection matrices are obtained between solutions at the origin and solutions at infinity.

Sur la fonction q-Gamma de Jackson

Summary. (On Jacksons q-Gamma function). Let

On the summability of the formal solutions for some PDEs with irregular singularity

q\in]0,1[

Zeros of entire functions and a problem of Ramanujan

; let us denote

Développement asymptotique q-Gevrey et fonction thêta de Jacobi

[x]=(1-q^x)/(1-q)

Une sommation discrète pour des équations aux q-différences linéaires et à coefficients analytiques: théorie générale et exemples

and

Local analytic classification of q-difference equations

(x;q)_\infty=\prod_{n\ge 0}(1-xq^n)

On

for

q

x\in{\Bbb C}

-summation and confluence

. Let