The general partial surgery formula for GM series

Let $L$ be a link with a well-defined GM series, and let $L'$ be obtained by partial $-1/r$ surgery on an unknot component, or by $\infty$-surgery in the corresponding case. Partial Surgery Formula. The Partial Surgery Theorem holds for any link with a well-defined GM series whenever the Laplace transform converges. The analogous statement holds for $\infty$-surgery. This extends the theorem proved for plumbed links, with convergence as the remaining restriction.