Formula:5793

Digital Library of Mathematical Functions ID 15.9.E6

${\displaystyle{\displaystyle U_{n}\left(x\right)=(n+1)F\left({-n,n+2\atop\frac{3}{2}};\frac{1-x}{2}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle U_{\NVar{n}}\left(\NVar{x}\right)}}$: Chebyshev polynomial of the second kind
• ${\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle n}}$: integer
 

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