Difference equation of the colored Jones polynomial for torus knot
Abstract
We prove that the N-colored Jones polynomial for the torus knot Ts,t satisfies the second order difference equation, which reduces to the first order difference equation for a case of T2,2m+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 T2,2m+1.
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