Formula:6516

Digital Library of Mathematical Functions ID 18.18.E29

${\displaystyle{\displaystyle\sum_{\ell=0}^{n}C^{(\lambda)}_{\ell}\left(x\right)C^{(\mu)}_{n-\ell}\left(x\right)=C^{(\lambda+\mu)}_{n}\left(x\right).}}$

Symbols List

• ${\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}\right)}}$: ultraspherical (or Gegenbauer) polynomial
• ${\displaystyle{\displaystyle\ell}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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