The colored Jones function is \(q\)-holonomic (Q2388869)

The authors show that the colored Jones function, a sequence of Laurent polynomials defined for a knot diagram and incorporating the Jones polynomials of \(K\) and its cables, has a property known as \(q\)-holonomicity for any knot \(K\). This generalizes a result previously known for some specific knots [see \textit{R. Gelca}, Math. Proc. Camb. Philos. Soc. 133, No. 2, 311--323 (2002; Zbl 1017.57002)]. The proof uses a state-sum formula to represent the colored Jones function as a multisum of hypergeometric functions.