$a=-n-\frac{2}{\pi }\sqrt{zn}-\frac{2z}{{\pi }^2}+12b+14+\frac{z^2\left(\frac{1}{3}-4{\pi }^{-2}\right)+z-{\left(b-1\right)}^2+\frac{1}{4}}{4\pi \sqrt{zn}}+\mathcal{O}\left(\frac{1}{n}\right)$