Uniform asymptotic expansions for Whittaker's confluent hypergeometric functions
SIAM Journal on Mathematical Analysis
Asymptotic estimates for Laguerre polynomials
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
On extreme zeros of classical orthogonal polynomials
Journal of Computational and Applied Mathematics
On the effect of correlation on the performance of dual diversity receivers in lognormal fading
IEEE Communications Letters
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Some of the work on the construction of inequalities and asymptotic approximations for the zeros λn,k(α), k = 1,2 .... ,n, of the Laguerre polynomial Lnα(x) as v = 4n + 2α + 2 → ∞, is reviewed and discussed. The cases when one or both parameters n and α unrestrictedly diverge are considered. Two new uniform asymptotic representations are presented: the first involves the positive zeros of the Bessel function Jα(x), and the second is in terms of the zeros of the Airy function Ai(x). They hold for k= 1,2 .... , [qn] and for k = [pn], [pn] + 1 ..... n, respectively, where p and q are fixed numbers in the interval (0, 1 ). Numerical results and comparisons are provided which favorably justify the consideration of the new approximations formulas.