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Please. Does anybody know a proof of this inequality $$\Big|\frac{n!\Gamma(\alpha+1)}{\Gamma(n+\alpha+1)} L^{\alpha}_n(x)\Big|\leq e^{\frac{x}{2}}$$ where $\alpha\geq0$ and $x\geq0$ and $L^{\alpha}_n$ is the n-th Laguerre polynomial. Thanks

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The inequality and its proof can be found in Chapter 10.18, Eq. (14), p.207 of

A. Erdelyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, "Higher Transcendental Functions", vol. 2, Bateman Manuscript Project (McGraw-Hill, New York, 1953).

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  • $\begingroup$ Thank you a lot@user111. $\endgroup$ – Kacdima Nov 12 '20 at 9:09

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