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We analyze the Moyal star product in deformation quantization from theresurgence theory perspective. By putting algebraic conditions on Boreltransforms, one can define the space of ``algebro-resurgent series'' (asubspace of $1$-Gevrey formal series in $i\hbar/2$ with coefficients in$C\{q,p\}$), which we show is stable under Moyal star product.

On the Moyal Star Product of Resurgent Series