Formula:6562

Digital Library of Mathematical Functions ID 18.21.E12

${\displaystyle{\displaystyle\lim_{\phi\to 0}P^{(\frac{1}{2}\alpha+\frac{1}{2})}_{n}\left(-(2\phi)^{-1}x;\phi\right)=L^{(\alpha)}_{n}\left(x\right).}}$

Symbols List

• ${\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}\right)}}$: Laguerre (or generalized Laguerre) polynomial
• ${\displaystyle{\displaystyle P^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x};\NVar{\phi}\right)}}$: Meixner–Pollaczek polynomial
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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