Abstract
Asymptotic expansions are derived for the inflection pointsj"vkof the Bessel functionJv(x), ask→ ∞ for fixedvand asv→ ∞ for fixedk. Also derived is an asymptotic expansion ofJv(j"vk) asv→ ∞. Finally, we prove thatj"vʎ≽v√2 ifʎ≽ (0.07041)v+ 0.25 andv≽ 7, which implies by a recent result of Lorch & Szego that the sequence {|Jv(j"vk)|} is decreasing, fork═ʎ,ʎ+ 1,ʎ+ 2,....
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