Formula:6269

Digital Library of Mathematical Functions ID 18.7.E4

${\displaystyle{\displaystyle U_{n}\left(x\right)=C^{(1)}_{n}\left(x\right)=\ifrac{(n+1)P^{(\frac{1}{2},\frac{1}{2})}_{n}\left(x\right)}{P^{(\frac{1}{2},\frac{1}{2})}_{n}\left(1\right)},}}$

Symbols List

• ${\displaystyle{\displaystyle U_{\NVar{n}}\left(\NVar{x}\right)}}$: Chebyshev polynomial of the second kind
• ${\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(\NVar{x}\right)}}$: Jacobi polynomial
• ${\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}\right)}}$: ultraspherical (or Gegenbauer) polynomial
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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