The asymptotic expansion conjecture for zeros of $d_2(B)$ in Heun equations

Let $d_2(B)$ be the function associated with the Heun equation, the confluent Heun equation, and the reduced confluent Heun equation, and let $D_k$ and $D_k^{[j],(k+j+1)}$ denote the coefficients defined by the corresponding expansions of the zeros of $c_{m+1}(B)$, for $k=0,1,2,\dots$. Zero-expansion conjecture. The zeros of $d_2(B)$ have the expansions

$$-D_k-\sum_{j=1}^{\infty}D_k^{[j],(k+j+1)}s^j$$

for $k=0,1,2,\dots$. This conjecture predicts that the zeros of $d_2(B)$ share the limiting formal expansions obtained from the zeros of $c_{m+1}(B)$ as the degree parameter becomes large, simultaneously for the Heun, confluent Heun, and reduced confluent Heun equations.