Notes on three conjectures involving the digamma and generalized digamma functions
Abstract In the paper, we solve one conjecture on an inequality involving digamma function, an open problem, and a conjecture on monotonicity of functions involving generalized digamma function. We also prove a new inequality for digamma function.
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-12-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-018-1936-z |
| _version_ | 1818969074928975872 |
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| author | Ladislav Matejíčka |
| author_facet | Ladislav Matejíčka |
| author_sort | Ladislav Matejíčka |
| collection | DOAJ |
| description | Abstract In the paper, we solve one conjecture on an inequality involving digamma function, an open problem, and a conjecture on monotonicity of functions involving generalized digamma function. We also prove a new inequality for digamma function. |
| first_indexed | 2024-12-20T14:14:49Z |
| format | Article |
| id | doaj.art-d4e73a69646248b39b425c7b193f0c0e |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-20T14:14:49Z |
| publishDate | 2018-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-d4e73a69646248b39b425c7b193f0c0e2022-12-21T19:38:04ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-12-012018111210.1186/s13660-018-1936-zNotes on three conjectures involving the digamma and generalized digamma functionsLadislav Matejíčka0Faculty of Industrial Technologies in Púchov, Trenčín University of Alexander Dubček in TrenčínAbstract In the paper, we solve one conjecture on an inequality involving digamma function, an open problem, and a conjecture on monotonicity of functions involving generalized digamma function. We also prove a new inequality for digamma function.http://link.springer.com/article/10.1186/s13660-018-1936-zDigamma function( p , k ) $(p, k)$ -digamma functionComplete monotonicityMonotonicityInequalities |
| spellingShingle | Ladislav Matejíčka Notes on three conjectures involving the digamma and generalized digamma functions Journal of Inequalities and Applications Digamma function ( p , k ) $(p, k)$ -digamma function Complete monotonicity Monotonicity Inequalities |
| title | Notes on three conjectures involving the digamma and generalized digamma functions |
| title_full | Notes on three conjectures involving the digamma and generalized digamma functions |
| title_fullStr | Notes on three conjectures involving the digamma and generalized digamma functions |
| title_full_unstemmed | Notes on three conjectures involving the digamma and generalized digamma functions |
| title_short | Notes on three conjectures involving the digamma and generalized digamma functions |
| title_sort | notes on three conjectures involving the digamma and generalized digamma functions |
| topic | Digamma function ( p , k ) $(p, k)$ -digamma function Complete monotonicity Monotonicity Inequalities |
| url | http://link.springer.com/article/10.1186/s13660-018-1936-z |
| work_keys_str_mv | AT ladislavmatejicka notesonthreeconjecturesinvolvingthedigammaandgeneralizeddigammafunctions |