\begin{table}
\begin{tabular}{|c|c|c|c|}
\hline
فرمول & محدوده تعریف & تابع وزن & نام \\
\hline

 $P_{k} ^{(\alpha ,\beta)} (x)=\sum_{v=0}^k\binom{k+\alpha}{k-v}\binom{k+\beta}{v}(\frac{x-1}{2})^v (\frac{x+1}{2})^{k-v}$ & $[-1,1]$ & $(1-x)^\alpha (1+x)^\beta , \alpha,\beta >-1$ & Jacobi \\

\hline
$G_{k} ^{(\lambda)} (x)=\sum_{m=0} ^{[\frac{k}{2}]} \frac{(-1)^m \Gamma(k-m+\lambda)(2x)^{k-2m}}{\Gamma(\lambda)\Gamma(m+1)\Gamma(k-2m+1)}$ & $[-1,1]$ & $(1-x^2)^\lambda ,\lambda >-1$ & Gegenbauer 
\\
\hline
$L_{k}(x)=\frac{e^x}{k!}\frac{d^k}{dx^k}(x^k e^{-x}) , L_{0}(x)=1$ & $[-1,1]$ & $1$ & Legender \\

\hline
$T_{k}(x)=cos(k~arc~cos~x)$ & $[-1,1]$ & $(1-x^2)^{-\frac{1}{2}}$ & (1) Chebyshev \\

\hline
$u_{k}(x)=\frac{sin((k+1)\theta)}{sin\theta} , x=cos\theta$ & $[-1,1]$ & $(1-x^2)^{\frac{1}{2}}$ &  (2) Chebyshev 
\\
\hline
$H_{0}(x)=1 , H_{k}(x)=(-1)^k e^{\frac{x^2}{2}}\frac{d^k}{dx^k}e^{-\frac{x^2}{2}}$ & $(-\infty ,+\infty)$ & $e^{-\frac{x^2}{2}}$ & Hermite \\

\hline
$L_{k} ^{(\lambda)} (x)=\frac{e^x x^{-\lambda}}{k!}\frac{d^k}{dx^k}(e^{-x} x^{k+\lambda})$ & $(0,+\infty)$ & $x^{\lambda} e^{-x} , \lambda >-1$ & Laguerre\\

\hline
\end{tabular}
\end{table}