The Integral Mittag-Leffler, Whittaker and Wright Functions
Integral Mittag-Leffler, Whittaker and Wright functions with integrands similar to those which already exist in mathematical literature are introduced for the first time. For particular values of parameters, they can be presented in closed-form. In most reported cases, these new integral functions a...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/24/3255 |
| _version_ | 1797502636388253696 |
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| author | Alexander Apelblat Juan Luis González-Santander |
| author_facet | Alexander Apelblat Juan Luis González-Santander |
| author_sort | Alexander Apelblat |
| collection | DOAJ |
| description | Integral Mittag-Leffler, Whittaker and Wright functions with integrands similar to those which already exist in mathematical literature are introduced for the first time. For particular values of parameters, they can be presented in closed-form. In most reported cases, these new integral functions are expressed as generalized hypergeometric functions but also in terms of elementary and special functions. The behavior of some of the new integral functions is presented in graphical form. By using the MATHEMATICA program to obtain infinite sums that define the Mittag-Leffler, Whittaker, and Wright functions and also their corresponding integral functions, these functions and many new Laplace transforms of them are also reported in the Appendices for integral and fractional values of parameters. |
| first_indexed | 2024-03-10T03:37:02Z |
| format | Article |
| id | doaj.art-462f0b3a50d449b391f4db0f7d94646e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:37:02Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-462f0b3a50d449b391f4db0f7d94646e2023-11-23T09:26:25ZengMDPI AGMathematics2227-73902021-12-01924325510.3390/math9243255The Integral Mittag-Leffler, Whittaker and Wright FunctionsAlexander Apelblat0Juan Luis González-Santander1Department of Chemical Engineering, Ben Gurion University of the Negev, Beer Sheva 84105, IsraelDepartment of Mathematics, Universidad de Oviedo, 33007 Oviedo, SpainIntegral Mittag-Leffler, Whittaker and Wright functions with integrands similar to those which already exist in mathematical literature are introduced for the first time. For particular values of parameters, they can be presented in closed-form. In most reported cases, these new integral functions are expressed as generalized hypergeometric functions but also in terms of elementary and special functions. The behavior of some of the new integral functions is presented in graphical form. By using the MATHEMATICA program to obtain infinite sums that define the Mittag-Leffler, Whittaker, and Wright functions and also their corresponding integral functions, these functions and many new Laplace transforms of them are also reported in the Appendices for integral and fractional values of parameters.https://www.mdpi.com/2227-7390/9/24/3255integral Mittag-Leffler functionsintegral Whittaker functionsintegral Wright functionsLaplace transforms |
| spellingShingle | Alexander Apelblat Juan Luis González-Santander The Integral Mittag-Leffler, Whittaker and Wright Functions Mathematics integral Mittag-Leffler functions integral Whittaker functions integral Wright functions Laplace transforms |
| title | The Integral Mittag-Leffler, Whittaker and Wright Functions |
| title_full | The Integral Mittag-Leffler, Whittaker and Wright Functions |
| title_fullStr | The Integral Mittag-Leffler, Whittaker and Wright Functions |
| title_full_unstemmed | The Integral Mittag-Leffler, Whittaker and Wright Functions |
| title_short | The Integral Mittag-Leffler, Whittaker and Wright Functions |
| title_sort | integral mittag leffler whittaker and wright functions |
| topic | integral Mittag-Leffler functions integral Whittaker functions integral Wright functions Laplace transforms |
| url | https://www.mdpi.com/2227-7390/9/24/3255 |
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