Formula:6517

Digital Library of Mathematical Functions ID 18.18.E30

${\displaystyle{\displaystyle\sum_{\ell=0}^{n}\frac{\ell+2\lambda}{2\lambda}C^{(\lambda)}_{\ell}\left(x\right)x^{n-\ell}=C^{(\lambda+1)}_{n}\left(x\right).}}$

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
 

Resources that cite this formula

No records found.