Inequalities for some basic hypergeometric functions
We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric functions with respect to the simultaneous shift of all its parameters. For a particular case of Heine’s basic hypergeometric function, we prove logarithmic c...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Petrozavodsk State University
2019-01-01
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| Series: | Проблемы анализа |
| Subjects: | |
| Online Access: | http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=5210&lang=ru |
| _version_ | 1818906550398353408 |
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| author | Kalmykov S. I. Karp D. B. |
| author_facet | Kalmykov S. I. Karp D. B. |
| author_sort | Kalmykov S. I. |
| collection | DOAJ |
| description | We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric functions with respect to the simultaneous shift of all its parameters. For a particular case of Heine’s basic hypergeometric function, we prove logarithmic concavity and convexity with respect to the bottom parameter. We, further, establish a linearization identity for the generalized Turánian formed by a particular case of Heine’s basic hypergeometric function. Its q = 1 case also appears to be new. |
| first_indexed | 2024-12-19T21:41:01Z |
| format | Article |
| id | doaj.art-5806b808ccb743d8a754dee137c14d8b |
| institution | Directory Open Access Journal |
| issn | 2306-3424 2306-3432 |
| language | English |
| last_indexed | 2024-12-19T21:41:01Z |
| publishDate | 2019-01-01 |
| publisher | Petrozavodsk State University |
| record_format | Article |
| series | Проблемы анализа |
| spelling | doaj.art-5806b808ccb743d8a754dee137c14d8b2022-12-21T20:04:40ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322019-01-018(26)1476410.15393/j3.art.2019.5210Inequalities for some basic hypergeometric functionsKalmykov S. I.0Karp D. B.1Far Eastern Federal University, Institute of Applied Mathematics, FEBRASFar Eastern Federal University, Institute of Applied Mathematics, FEBRASWe establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric functions with respect to the simultaneous shift of all its parameters. For a particular case of Heine’s basic hypergeometric function, we prove logarithmic concavity and convexity with respect to the bottom parameter. We, further, establish a linearization identity for the generalized Turánian formed by a particular case of Heine’s basic hypergeometric function. Its q = 1 case also appears to be new.http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=5210&lang=rubasic hypergeometric functionlog-convexitylog-concavitymultiplicative concavitygeneralized Turanianq-hypergeometric identity |
| spellingShingle | Kalmykov S. I. Karp D. B. Inequalities for some basic hypergeometric functions Проблемы анализа basic hypergeometric function log-convexity log-concavity multiplicative concavity generalized Turanian q-hypergeometric identity |
| title | Inequalities for some basic hypergeometric functions |
| title_full | Inequalities for some basic hypergeometric functions |
| title_fullStr | Inequalities for some basic hypergeometric functions |
| title_full_unstemmed | Inequalities for some basic hypergeometric functions |
| title_short | Inequalities for some basic hypergeometric functions |
| title_sort | inequalities for some basic hypergeometric functions |
| topic | basic hypergeometric function log-convexity log-concavity multiplicative concavity generalized Turanian q-hypergeometric identity |
| url | http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=5210&lang=ru |
| work_keys_str_mv | AT kalmykovsi inequalitiesforsomebasichypergeometricfunctions AT karpdb inequalitiesforsomebasichypergeometricfunctions |