${\stackrel{˜}{h}}_{n}^{a,b}\left(x;N\right)$ ${\stackrel{˜}{m}}_{n}^{\beta ,\mu }\left(x\right)$ $A$ $\frac{n}{a+b+2n-1}\ast \frac{a+b+n}{a+b+2n}$ $\frac{\mu }{\mu -1}$ $B$ $\begin{array}{l}x-\frac{a-b+2N-2}{4}\\ -\frac{\left({b}^{2}+{a}^{2}\right)\left(a+b+2N\right)}{4\left(a+b+2n-2\right)\left(a+b+2n\right)}\end{array}$ $\frac{x-x\mu -n+1-\mu n+\mu -\beta \mu }{1-\mu }$ $C$ $\begin{array}{l}-\frac{\left(a+n-1\right)\left(N-n+2\right)}{a+b+2n-1}\\ \ast \frac{\left(a+b+N+n-1\right)\left(N-n+1\right)}{a+b+2n-1}\end{array}$ $-\frac{\left(n-1\right)\left(n-2+\beta \right)}{1-\mu }$ $D$ $\sqrt{\frac{n\left(a+b+n\right)\left(a+b+2n+1\right)}{\left(a+n\right)\left(b+n\right)\left(a+b+n+N\right)\left(N-n\right)\left(a+b+2n-1\right)}}$ $\sqrt{\frac{\mu }{n\left(\beta +n-1\right)}}$ $E$ $\begin{array}{l}\sqrt{\frac{n\left(n-1\right)\left(a+b+n\right)}{\left(a+n\right)\left(b+n\right)\left(a+n+1\right)\left(b+n+1\right)\left(N-n+1\right)\left(N-n\right)}}\\ \ast \sqrt{\frac{\left(a+b+n-1\right)\left(a+b+2n\right)}{\left(a+b+2n-3\right)\left(a+b+2n-1\right)}}\end{array}$ $\sqrt{\frac{{\mu }^{2}}{\left(n-1\right)\left(\beta +n-2\right)n\left(\beta +n-1\right)}}$