A note on monotonicity property of Bessel functions
A theorem of Lorch, Muldoon and Szegö states that the sequence {∫jα,kjα,k+1t−α|Jα(t)|dt}k=1∞ is decreasing for α>−1/2, where Jα(t) the Bessel function of the first kind order α and jα,k its kth positive root. This monotonicity property implies Szegö's inequality ∫0xt−αJα(t)dt≥0, when α≥α′ an...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171297000756 |
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| Summary: | A theorem of Lorch, Muldoon and Szegö states that the sequence
{∫jα,kjα,k+1t−α|Jα(t)|dt}k=1∞
is decreasing for α>−1/2, where Jα(t) the Bessel function of the first kind order α and jα,k its kth
positive root. This monotonicity property implies Szegö's inequality
∫0xt−αJα(t)dt≥0,
when α≥α′ and α′ is the unique solution of ∫0jα,2t−αJα(t)dt=0. |
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| ISSN: | 0161-1712 1687-0425 |