Inequalities for Laguerre functions
<p/> <p>The main published inequality for Laguerre functions <inline-formula><graphic file="1029-242X-1997-936095-i1.gif"/></inline-formula> seems to be for Laguerre polynomials <inline-formula><graphic file="1029-242X-1997-936095-i2.gif"/&g...
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| Format: | Article |
| Language: | English |
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SpringerOpen
1997-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/1/936095 |
| _version_ | 1818387623636369408 |
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| author | Love ER |
| author_facet | Love ER |
| author_sort | Love ER |
| collection | DOAJ |
| description | <p/> <p>The main published inequality for Laguerre functions <inline-formula><graphic file="1029-242X-1997-936095-i1.gif"/></inline-formula> seems to be for Laguerre polynomials <inline-formula><graphic file="1029-242X-1997-936095-i2.gif"/></inline-formula> only; it is [2: 10.18(3)]: <inline-formula><graphic file="1029-242X-1997-936095-i3.gif"/></inline-formula>This paper presents several inequalities for Laguerre polynomials <inline-formula><graphic file="1029-242X-1997-936095-i4.gif"/></inline-formula> and Laguerre functions <inline-formula><graphic file="1029-242X-1997-936095-i5.gif"/></inline-formula>, most of which do not seem to be in the existing literature. The corresponding inequalities for confluent hypergeometric functions are noted.</p> <p>For our work on expansions in series of Laguerre functions, M.N. Hunter and I needed an inequality for <inline-formula><graphic file="1029-242X-1997-936095-i6.gif"/></inline-formula> when re <inline-formula><graphic file="1029-242X-1997-936095-i7.gif"/></inline-formula> and re <inline-formula><graphic file="1029-242X-1997-936095-i8.gif"/></inline-formula> is large. The only extensions of the above inequality that we could obtain had multiples of <inline-formula><graphic file="1029-242X-1997-936095-i9.gif"/></inline-formula> on the right hand side instead of <inline-formula><graphic file="1029-242X-1997-936095-i10.gif"/></inline-formula>. This paper goes on to show that this is inevitable for non-integral <inline-formula><graphic file="1029-242X-1997-936095-i11.gif"/></inline-formula>, in that <inline-formula><graphic file="1029-242X-1997-936095-i12.gif"/></inline-formula> can exceed a multiple of <inline-formula><graphic file="1029-242X-1997-936095-i13.gif"/></inline-formula> for every fixed <inline-formula><graphic file="1029-242X-1997-936095-i14.gif"/></inline-formula> if <inline-formula><graphic file="1029-242X-1997-936095-i15.gif"/></inline-formula> is sufficiently large.</p> |
| first_indexed | 2024-12-14T04:12:53Z |
| format | Article |
| id | doaj.art-f16bfbbe840547bca833201a54845c6f |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-14T04:12:53Z |
| publishDate | 1997-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-f16bfbbe840547bca833201a54845c6f2022-12-21T23:17:37ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X1997-01-0119973936095Inequalities for Laguerre functionsLove ER<p/> <p>The main published inequality for Laguerre functions <inline-formula><graphic file="1029-242X-1997-936095-i1.gif"/></inline-formula> seems to be for Laguerre polynomials <inline-formula><graphic file="1029-242X-1997-936095-i2.gif"/></inline-formula> only; it is [2: 10.18(3)]: <inline-formula><graphic file="1029-242X-1997-936095-i3.gif"/></inline-formula>This paper presents several inequalities for Laguerre polynomials <inline-formula><graphic file="1029-242X-1997-936095-i4.gif"/></inline-formula> and Laguerre functions <inline-formula><graphic file="1029-242X-1997-936095-i5.gif"/></inline-formula>, most of which do not seem to be in the existing literature. The corresponding inequalities for confluent hypergeometric functions are noted.</p> <p>For our work on expansions in series of Laguerre functions, M.N. Hunter and I needed an inequality for <inline-formula><graphic file="1029-242X-1997-936095-i6.gif"/></inline-formula> when re <inline-formula><graphic file="1029-242X-1997-936095-i7.gif"/></inline-formula> and re <inline-formula><graphic file="1029-242X-1997-936095-i8.gif"/></inline-formula> is large. The only extensions of the above inequality that we could obtain had multiples of <inline-formula><graphic file="1029-242X-1997-936095-i9.gif"/></inline-formula> on the right hand side instead of <inline-formula><graphic file="1029-242X-1997-936095-i10.gif"/></inline-formula>. This paper goes on to show that this is inevitable for non-integral <inline-formula><graphic file="1029-242X-1997-936095-i11.gif"/></inline-formula>, in that <inline-formula><graphic file="1029-242X-1997-936095-i12.gif"/></inline-formula> can exceed a multiple of <inline-formula><graphic file="1029-242X-1997-936095-i13.gif"/></inline-formula> for every fixed <inline-formula><graphic file="1029-242X-1997-936095-i14.gif"/></inline-formula> if <inline-formula><graphic file="1029-242X-1997-936095-i15.gif"/></inline-formula> is sufficiently large.</p>http://www.journalofinequalitiesandapplications.com/content/1/936095Laguerre polynomialLaguerre functionconfluent hypergeometric functionfractional integration |
| spellingShingle | Love ER Inequalities for Laguerre functions Journal of Inequalities and Applications Laguerre polynomial Laguerre function confluent hypergeometric function fractional integration |
| title | Inequalities for Laguerre functions |
| title_full | Inequalities for Laguerre functions |
| title_fullStr | Inequalities for Laguerre functions |
| title_full_unstemmed | Inequalities for Laguerre functions |
| title_short | Inequalities for Laguerre functions |
| title_sort | inequalities for laguerre functions |
| topic | Laguerre polynomial Laguerre function confluent hypergeometric function fractional integration |
| url | http://www.journalofinequalitiesandapplications.com/content/1/936095 |
| work_keys_str_mv | AT loveer inequalitiesforlaguerrefunctions |