${\tilde{t}}_n\left(x;N\right)$

${\tilde{k}}_n\left(x;p,N\right)$

${\tilde{c}}_n^{a_1}\left(x\right)$

${\tilde{p}}_0\left(x\right)$

$\frac{1}{\sqrt{N}}$

$\sqrt{\frac{N!p^x{\left(1-p\right)}^{N-x}}{x!\left(N-x\right)!}}$

$\sqrt{\frac{{\text{e}}^{-\mu }{\mu }^x}{x!}}$

${\tilde{p}}_1\left(x\right)$

$\left(N-1-2x\right)\sqrt{\frac{3}{N\left(N^2-1\right)}}$

$\begin{array}{l}-p\left(N-x\right)+x\left(1-p\right)\\ \ast \sqrt{\frac{\left(N-1\right)!p^{x-1}{\left(1-p\right)}^{N-x-1}}{x!\left(N-x\right)!}}\end{array}$

$\frac{\mu -x}{\mu }\sqrt{\frac{{\text{e}}^{-\mu }{\mu }^{x+1}}{x!}}$