Formula:6483

Digital Library of Mathematical Functions ID 18.17.E45

${\displaystyle{\displaystyle(n+\tfrac{1}{2})(1+x)^{\frac{1}{2}}\int_{-1}^{x}(x-t)^{-\frac{1}{2}}P_{n}\left(t\right)\mathrm{d}t=T_{n}\left(x\right)+T_{n+1}\left(x\right),}}$

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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