DLMF:18.7.E22 (Q5590)

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DLMF:18.7.E22
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    lim α P n ( α , β ) ( ( 2 x / α ) - 1 ) = ( - 1 ) n L n ( β ) ( x ) . subscript 𝛼 Jacobi-polynomial-P 𝛼 𝛽 𝑛 2 𝑥 𝛼 1 superscript 1 𝑛 Laguerre-polynomial-L 𝛽 𝑛 𝑥 {\displaystyle{\displaystyle\lim_{\alpha\to\infty}P^{(\alpha,\beta)}_{n}\left(% (2x/\alpha)-1\right)=(-1)^{n}L^{(\beta)}_{n}\left(x\right).}}
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