International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 561-566
A note on monotonicity property of Bessel functions
1Department of Pure Mathematics, The University of Adelaide, Adelaide 5005, Australia
2Department of Mathematics and Statistics, University of Cyprus, P.O. Box 537, Nicosia 1678, Cyprus
Received 18 September 1995
Copyright © 1997 Stamatis Koumandos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A theorem of Lorch, Muldoon and Szegö states that the sequence
is decreasing for , where the Bessel function of the first kind order and its th
positive root. This monotonicity property implies Szegö's inequality
when and is the unique solution of .
We give a new and simpler proof of these classical results by expressing the above Bessel function
integral as an integral involving elementary functions.