The asymptotic behavior of Jacobi polynomials Pₙα + an,β + bn (x) and Laguerre polynomials Lₙα + an (b + nx) is found when n → ∞ and a, b, α, $beta$ are real constants, $a > - 1$, $b > - 1$, and x is a real variable.
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Chen et al. (1991) studied this question.
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