Inequalities for orthonormal Laguerre polynomials

Let M"k^@a(x)=L"k^(^@a^)(x)^2e^-^xx^@a^+^1, where L"k^(^@a^)(x) is the orthonormal Laguerre polynomial of degree k. For @a>=24 we will establish the following inequality 10^-^8=0M"k^@a(x) =35, and the lower one for k>=2x10^1^0. Sharp pointwise estimates on M"k^@a and related functions for x>=0 are also given.

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