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In this paper we prove that the $r$-th ADO polynomial of a knot, for $r$ apower of prime number, can be expanded as Vassiliev invariants with values in$\mathbb{Z}$. Nevertheless this expansion is not unique and not easilycomputable. We can obtain a unique computable expansion, but we only get $r$adic topological Vassiliev invariants as coefficients. To do so, we exploit thefact that the colored Jones polynomials can be decomposed as Vassilievinvariants and we tranpose it to ADO using the unified knot invariantrecovering both ADO and colored Jones defined in arXiv:2003.09854. Finally weprove some asymptotic behavior of the ADO polynomials modulo $r$ as $r$ goes toinfinity.

Vassiliev invariants for knots from the ADO polynomials