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- W22207813 abstract "In this paper we obtain two asymptotic formulas for the zeros <m:math> <m:mrow> <m:msubsup> <m:mi>λ</m:mi> <m:mrow> <m:mi>n</m:mi><m:mo>,</m:mo><m:mi>k</m:mi> </m:mrow> <m:mrow> <m:mo stretchy='false'>(</m:mo><m:mi>α</m:mi><m:mo stretchy='false'>)</m:mo> </m:mrow> </m:msubsup> <m:mo>,</m:mo><m:mi>k</m:mi><m:mo>=</m:mo><m:mn>1</m:mn><m:mo>,</m:mo><m:mn>2</m:mn><m:mo>,</m:mo><m:mo>…</m:mo><m:mo>,</m:mo><m:mi>n</m:mi><m:mo>,</m:mo> </m:mrow> </m:math> $$ lambda _{n,k}^{(alpha )},k = 1,2, ldots ,n, $$ of the Laguerre polynomials <m:math> <m:mrow> <m:msubsup> <m:mi>L</m:mi> <m:mi>n</m:mi> <m:mrow> <m:mo stretchy='false'>(</m:mo><m:mi>α</m:mi><m:mo stretchy='false'>)</m:mo> </m:mrow> </m:msubsup> <m:mo stretchy='false'>(</m:mo><m:mi>x</m:mi><m:mo stretchy='false'>)</m:mo> </m:mrow> </m:math> $$ L_n^{(alpha )}(x) $$ , as n → ∞ and α is fixed. These formulas are in terms of the zeros of the Bessel function J (x) and in terms of the zeros of the Airy function Ai(χ). 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)." @default.
- W22207813 created "2016-06-24" @default.
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- W22207813 date "1988-01-01" @default.
- W22207813 modified "2023-09-23" @default.
- W22207813 title "Uniform Approximations for the Zeros of Laguerre Polynomials" @default.
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- W22207813 doi "https://doi.org/10.1007/978-3-0348-6303-2_12" @default.
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