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Asymptotic Behaviour of the Inflection Points of Bessel Functions

R. Wong and T. Lang
Proceedings: Mathematical and Physical Sciences
Vol. 431, No. 1883 (Dec. 8, 1990), pp. 509-518
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/51957
Page Count: 10
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Asymptotic Behaviour of the Inflection Points of Bessel Functions
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Abstract

Asymptotic expansions are derived for the inflection points jν k′ ′ of the Bessel function Jν(x), as k → ∞ for fixed ν and as ν → ∞ for fixed k. Also derived is an asymptotic expansion of Jν(jν k′ ′) as ν → ∞ . Finally, we prove that jν λ′ ′≥ ν √ 2 if λ ≥ (0.07041)ν + 0.25 and ν ≥ 7, which implies by a recent result of Lorch & Szego that the sequence {|Jν(jν k′ ′)|} is decreasing, for k = λ , λ +1, λ +2, ... .

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