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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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171297000756 |
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| _version_ | 1832562762277978112 |
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| author | Stamatis Koumandos |
| author_facet | Stamatis Koumandos |
| author_sort | Stamatis Koumandos |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b9e9b54013504260a7c695a370180c0c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b9e9b54013504260a7c695a370180c0c2025-02-03T01:21:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-0120356156610.1155/S0161171297000756A note on monotonicity property of Bessel functionsStamatis Koumandos0Department of Pure Mathematics, The University of Adelaide, Adelaide 5005, AustraliaA 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.http://dx.doi.org/10.1155/S0161171297000756Bessel functionspositive integral of Besel functionsmonotonicity property of Bessel functions. |
| spellingShingle | Stamatis Koumandos A note on monotonicity property of Bessel functions International Journal of Mathematics and Mathematical Sciences Bessel functions positive integral of Besel functions monotonicity property of Bessel functions. |
| title | A note on monotonicity property of Bessel functions |
| title_full | A note on monotonicity property of Bessel functions |
| title_fullStr | A note on monotonicity property of Bessel functions |
| title_full_unstemmed | A note on monotonicity property of Bessel functions |
| title_short | A note on monotonicity property of Bessel functions |
| title_sort | note on monotonicity property of bessel functions |
| topic | Bessel functions positive integral of Besel functions monotonicity property of Bessel functions. |
| url | http://dx.doi.org/10.1155/S0161171297000756 |
| work_keys_str_mv | AT stamatiskoumandos anoteonmonotonicitypropertyofbesselfunctions AT stamatiskoumandos noteonmonotonicitypropertyofbesselfunctions |