A note on monotonicity property of Bessel functions

Stamatis Koumandos

International Journal of Mathematics and Mathematical Sciences, 1997, vol. 20, 1-6

Abstract:

A theorem of Lorch, Muldoon and Szegö states that the sequence { ∫ j α , k j α , k + 1 t − α | J α ( t ) | d t } k = 1 ∞ is decreasing for α > − 1 / 2 , where J α ( t ) the Bessel function of the first kind order α and j α , k its k th positive root. This monotonicity property implies Szegö's inequality ∫ 0 x t − α J α ( t ) d t ≥ 0 , when α ≥ α ′ and α ′ is the unique solution of ∫ 0 j α , 2 t − α J α ( t ) d t = 0 .

We give a new and simpler proof of these classical results by expressing the above Bessel function integral as an integral involving elementary functions.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:683727

DOI: 10.1155/S0161171297000756

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