Formula:6555

Digital Library of Mathematical Functions ID 18.21.E5

${\displaystyle{\displaystyle\lim_{N\to\infty}Q_{n}\left(Nx;\alpha,\beta,N\right)=\frac{P^{(\alpha,\beta)}_{n}\left(1-2x\right)}{P^{(\alpha,\beta)}_{n}\left(1\right)}.}}$

Symbols List

• ${\displaystyle{\displaystyle Q_{\NVar{n}}\left(\NVar{x};\NVar{\alpha},\NVar{\beta},\NVar{N}\right)}}$: Hahn polynomial
• ${\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(\NVar{x}\right)}}$: Jacobi polynomial
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle N}}$: positive integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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