Formula:6484

Digital Library of Mathematical Functions ID 18.17.E46

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle (n+\tfrac{1}{2})(1-x)^{\frac{1}{2}}\int_{x}^{1}(t-x)^{-\frac{1}{2}}\LegendrepolyP{n}@{t}\diff{t}=\ChebyshevpolyT{n}@{x}-\ChebyshevpolyT{n+1}@{x}.}

Symbols List

• ${\displaystyle{\displaystyle T_{\NVar{n}}\left(\NVar{x}\right)}}$: Chebyshev polynomial of the first kind
• ${\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}$: Legendre polynomial
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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