Stable quotient holomorphic anomaly equations for local \u03b2c0^2

Let $K\mathbb{P}^2$ be the local projective plane, let $T=I^{K\mathbb{P}^2}_1(q)$ be the mirror coordinate, and let $\mathcal{F}^{\mathsf{SQ}}_g$ denote its genus-$g$ stable quotient invariants. Let $A_2$, $C_1$, and the derivatives with respect to $T$ be as defined in the source. Holomorphic anomaly equation for local $\mathbb{P}^2$. For $g\geq2$,

$$\frac{1}{C_1^2}\frac{\partial\mathcal{F}^{\mathsf{SQ}}_g}{\partial A_2}=\frac{1}{2}\sum_{i=1}^{g-1}\frac{\partial\mathcal{F}^{\mathsf{SQ}}_{g-i}}{\partial T}\frac{\partial\mathcal{F}^{\mathsf{SQ}}_i}{\partial T}+\frac{1}{2}\frac{\partial^2\mathcal{F}^{\mathsf{SQ}}_{g-1}}{\partial T^2}.$$

These equations describe the genus recursion predicted by the holomorphic anomaly formalism for stable quotient invariants; no resolution is supplied in the given text.