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The colored Jones function of a knot is a sequence of Laurent polynomials. Itwas shown by TTQ. Le and the author that such sequences are $q$-holonomic, thatis, they satisfy linear $q$-difference equations with coefficients Laurentpolynomials in $q$ and $q^n$. We show from first principles that $q$-holonomicsequences give rise to modules over a $q$-Weyl ring. Frohman-Gelca-LoFaro haveidentified the latter ring with the ring of even functions of the quantumtorus, and with the Kauffman bracket skein module of the torus. Via thisidentification, we study relations among the orthogonal, peripheral andrecursion ideal of the colored Jones function, introduced by the abovementioned authors. In the second part of the paper, we convert the linear$q$-difference equations of the colored Jones function in terms of a hierarchyof linear ordinary differential equations for its loop expansion. Thisconversion is a version of the WKB method, and may shed some information on theproblem of asymptotics of the colored Jones function of a knot.Final version.To appear in the Journal of Knot Theory and its Ramifications.

DIFFERENCE AND DIFFERENTIAL EQUATIONS FOR THE COLORED JONES FUNCTION