DLMF:18.11.E6

MaRDI QIDQ6337

• Label: DLMF:18.11.E6

Digital Library of Mathematical Functions ID 18.11.E6

${\displaystyle{\displaystyle\lim_{n\to\infty}\frac{1}{n^{\alpha}}L^{(\alpha)}_{n}\left(\frac{z}{n}\right)=\frac{1}{z^{\frac{1}{2}\alpha}}J_{\alpha}\left(2z^{\frac{1}{2}}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}\right)}}$: Laguerre (or generalized Laguerre) polynomial
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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