Formula:6504

Digital Library of Mathematical Functions ID 18.18.E17

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

Symbols List

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

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