Gold 80

Orthogonal polynomials

Gold ID: 80
Link: https://sigir21.wmflabs.org/wiki/Orthogonal_polynomials#math.133.8
Formula: $P_{n} (x) = c_{n} \det [\begin{matrix} m_{0} & m_{1} & m_{2} & \dots & m_{n} \\ m_{1} & m_{2} & m_{3} & \dots & m_{n + 1} \\ ⋮ & ⋮ \\ m_{n - 1} & m_{n} & m_{n + 1} & \dots & m_{2 n - 1} \\ 1 & x & x^{2} & \dots & x^{n} \end{matrix}]$
TeX Source: P_n(x) = c_n \, \det \begin{bmatrix}m_0 & m_1 & m_2 &\cdots & m_n \\m_1 & m_2 & m_3 &\cdots & m_{n+1} \\&&\vdots&& \vdots \\m_{n-1} &m_n& m_{n+1} &\cdots &m_{2n-1}\\1 & x & x^2 & \cdots & x^n\end{bmatrix}

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
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Translation: P_n(x) = c_n \det \begin{bmatrix}m_0 & m_1 & m_2 &\cdots & m_n \\m_1 & m_2 & m_3 &\cdots & m_{n+1} \\&&\vdots&& \vdots \\m_{n-1} &m_n& m_{n+1} &\cdots &m_{2n-1}\\1 & x & x^2 & \cdots & x^n\end{bmatrix}
Expected (Gold Entry): P_n(x) = c_n \det \begin{bmatrix}m_0 & m_1 & m_2 &\cdots & m_n \\m_1 & m_2 & m_3 &\cdots & m_{n+1} \\&&\vdots&& \vdots \\m_{n-1} &m_n& m_{n+1} &\cdots &m_{2n-1}\\1 & x & x^2 & \cdots & x^n\end{bmatrix}