Formula:KLS:09.13:15

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formula in Bessel

Formula:KLS:09.13:16 >>

${\displaystyle{\displaystyle{\displaystyle L^{\alpha}_{n}\left(x\right)=\frac{(-x)^{n}}{n!}y_{n}\!\left(2x^{-1};-2n-\alpha-1\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : Laguerre (or generalized Laguerre) polynomial : http://dlmf.nist.gov/18.3#T1.t1.r27
${\displaystyle{\displaystyle{\displaystyle y_{n}}}}$ : Bessel polynomial : http://dlmf.nist.gov/18.34#E1

Bibliography

Equation in Section 9.13 of KLS.

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