On Modifications of the Gamma Function by Using Mittag-Leffler Function
Mittag-Leffler function is a natural generalization of the exponential function. Recent applications of Mittag-Leffler function have reshaped the scientific literature due to its fractional effects that cannot be obtained by using exponential function. Present motivation is to define a new special f...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9991762 |
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| _version_ | 1832566415603793920 |
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| author | Asifa Tassaddiq Abdulrahman Alruban |
| author_facet | Asifa Tassaddiq Abdulrahman Alruban |
| author_sort | Asifa Tassaddiq |
| collection | DOAJ |
| description | Mittag-Leffler function is a natural generalization of the exponential function. Recent applications of Mittag-Leffler function have reshaped the scientific literature due to its fractional effects that cannot be obtained by using exponential function. Present motivation is to define a new special function by modification in the original gamma function with Mittag-Leffler function. Properties of this modified function are discussed by investigating a new series representation involving delta function. Hence, the results are also validated with the earlier obtained results for gamma function as special cases. Furthermore, the new function is used to generate a probability density function, and its statistical properties are explored. Similar properties of existing distributions can be deduced. |
| format | Article |
| id | doaj-art-81034c0bb5bd46b7b8b366cdfff3b00b |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-81034c0bb5bd46b7b8b366cdfff3b00b2025-02-03T01:04:10ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/99917629991762On Modifications of the Gamma Function by Using Mittag-Leffler FunctionAsifa Tassaddiq0Abdulrahman Alruban1Department of Basic Sciences and Humanities, College of Computer and Information Sciences, Majmaah University, Al-Majmaah 11952, Saudi ArabiaDepartment of Information Technology, College of Computer and Information Sciences, Majmaah University, Al-Majmaah 11952, Saudi ArabiaMittag-Leffler function is a natural generalization of the exponential function. Recent applications of Mittag-Leffler function have reshaped the scientific literature due to its fractional effects that cannot be obtained by using exponential function. Present motivation is to define a new special function by modification in the original gamma function with Mittag-Leffler function. Properties of this modified function are discussed by investigating a new series representation involving delta function. Hence, the results are also validated with the earlier obtained results for gamma function as special cases. Furthermore, the new function is used to generate a probability density function, and its statistical properties are explored. Similar properties of existing distributions can be deduced.http://dx.doi.org/10.1155/2021/9991762 |
| spellingShingle | Asifa Tassaddiq Abdulrahman Alruban On Modifications of the Gamma Function by Using Mittag-Leffler Function Journal of Mathematics |
| title | On Modifications of the Gamma Function by Using Mittag-Leffler Function |
| title_full | On Modifications of the Gamma Function by Using Mittag-Leffler Function |
| title_fullStr | On Modifications of the Gamma Function by Using Mittag-Leffler Function |
| title_full_unstemmed | On Modifications of the Gamma Function by Using Mittag-Leffler Function |
| title_short | On Modifications of the Gamma Function by Using Mittag-Leffler Function |
| title_sort | on modifications of the gamma function by using mittag leffler function |
| url | http://dx.doi.org/10.1155/2021/9991762 |
| work_keys_str_mv | AT asifatassaddiq onmodificationsofthegammafunctionbyusingmittaglefflerfunction AT abdulrahmanalruban onmodificationsofthegammafunctionbyusingmittaglefflerfunction |