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$\int_{a}^{b}p_{m}(x)p_{n}(x)w(x)\,dx% =0,\quad m\neq n}}$

Constraint(s): $m,n\in\{0,1,2,\ldots\}}}$

$0<\int_{a}^{b}x^{2n}w(x)\,dx<\infty% \quad\textrm{for all}}}$

Constraint(s): $n\in\{0,1,2,\ldots\}}}$

$0<\int_{a}^{b}x^{2n}\,d\alpha(x)<% \infty\quad\textrm{for all}}}$

Constraint(s): $n\in\{0,1,2,\ldots\}}}$

$\sum_{x\in X}p_{m}(x)p_{n}(x)w_{x}=0% ,\quad m\neq n}}$

Constraint(s): $m,n\in\{0,1,2,\ldots\}}}$

$\sum_{x\in X}p_{m}(x)p_{n}(x)w_{x}=0% ,\quad m\neq n}}$

Constraint(s): $m,n\in\{0,1,2,\ldots,N\}}}$

$\sigma_{n}=\int_{a}^{b}\left\{p_{n}(% x)\right\}^{2}w(x)\,dx}}$

Constraint(s): $n=0,1,2,\ldots}}$

$\sigma_{n}=\sum_{x\in X}\left\{p_{n}% (x)\right\}^{2}w_{x}}}$

Constraint(s): $n=0,1,2,\ldots}}$

$\sigma_{n}=\sum_{x\in X}\left\{p_{n}% (x)\right\}^{2}w_{x}}}$

Constraint(s): $n=0,1,2,\ldots,N}}$

$p_{n}(x)=k_{n}x^{n}+\,\textrm{lower% order terms}}}$

Constraint(s): $n=0,1,2,\ldots}}$

$\,\delta_{m,n}:=\left\{\begin{array}% []{ll}0,&m\neq n,\\ 1,&m=n,\end{array}\right.}}$

Constraint(s): $m,n\in\{0,1,2,\ldots\}}}$

$\int_{a}^{b}p_{m}(x)p_{n}(x)w(x)\,dx% =\sigma_{n}\,\delta_{m,n}}}$

Constraint(s): $m,n\in\{0,1,2,\ldots\}}}$

$\sum_{x\in X}p_{m}(x)p_{n}(x)w_{x}=% \sigma_{n}\,\delta_{m,n}}}$

Constraint(s): $m,n\in\{0,1,2,\ldots,N\}}}$