Difference equation of the colored Jones polynomial for torus knot
arXiv:math/0403224 · doi:10.1142/S0129167X04002582
Abstract
We prove that the N-colored Jones polynomial for the torus knot T_{s,t} satisfies the second order difference equation, which reduces to the first order difference equation for a case of T_{2,2m+1}. We show that the A-polynomial of the torus knot can be derived from this difference equation. Also constructed is a q-hypergeometric type expression of the colored Jones polynomial for T_{2,2m+1}.
7 pages