DLMF:18.7.E15

MaRDI QIDQ6280

• Label: DLMF:18.7.E15

Digital Library of Mathematical Functions ID 18.7.E15

${\displaystyle{\displaystyle C^{(\lambda)}_{2n}\left(x\right)=\frac{{\left(\lambda\right)_{n}}}{{\left(\tfrac{1}{2}\right)_{n}}}P^{(\lambda-\frac{1}{2},-\frac{1}{2})}_{n}\left(2x^{2}-1\right),}}$

Symbols List

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

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