The Bessel equation on the quantum calculus
A large number of the most diverse problems related to almost all the most important branches of mathematical physics and designed to answer topical technical questions are associated with the use of Bessel functions. This paper introduces a h-difference equation analogue of the Bessel differential...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2022-09-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/541 |
| _version_ | 1797372733821026304 |
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| author | S. Shaimardan N.S. Tokmagambetov Y. Aikyn |
| author_facet | S. Shaimardan N.S. Tokmagambetov Y. Aikyn |
| author_sort | S. Shaimardan |
| collection | DOAJ |
| description |
A large number of the most diverse problems related to almost all the most important branches of mathematical physics and designed to answer topical technical questions are associated with the use of Bessel functions. This paper introduces a h-difference equation analogue of the Bessel differential equation and investigates the properties of its solution, which is express using the Frobenius method by assuming a generalized power series. The authors find discrete analogue formulas for Bessel function and the h-Neumann function and these are solutions presented by a series with the h-fractional function th(α). Lastly they obtain the linear dependencies between h-functions Bessel on Ta .
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| first_indexed | 2024-03-08T18:39:09Z |
| format | Article |
| id | doaj.art-97e600b6b6804ad0a859668a1bec1013 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:39:09Z |
| publishDate | 2022-09-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-97e600b6b6804ad0a859668a1bec10132023-12-29T10:19:15ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112022-09-01107310.31489/2022m3/132-144The Bessel equation on the quantum calculusS. ShaimardanN.S. TokmagambetovY. Aikyn A large number of the most diverse problems related to almost all the most important branches of mathematical physics and designed to answer topical technical questions are associated with the use of Bessel functions. This paper introduces a h-difference equation analogue of the Bessel differential equation and investigates the properties of its solution, which is express using the Frobenius method by assuming a generalized power series. The authors find discrete analogue formulas for Bessel function and the h-Neumann function and these are solutions presented by a series with the h-fractional function th(α). Lastly they obtain the linear dependencies between h-functions Bessel on Ta . http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/541Bessel functionmodified Bessel functionBessel difference equationh-calculusthe h-derivative and h-fractional function |
| spellingShingle | S. Shaimardan N.S. Tokmagambetov Y. Aikyn The Bessel equation on the quantum calculus Қарағанды университетінің хабаршысы. Математика сериясы Bessel function modified Bessel function Bessel difference equation h-calculus the h-derivative and h-fractional function |
| title | The Bessel equation on the quantum calculus |
| title_full | The Bessel equation on the quantum calculus |
| title_fullStr | The Bessel equation on the quantum calculus |
| title_full_unstemmed | The Bessel equation on the quantum calculus |
| title_short | The Bessel equation on the quantum calculus |
| title_sort | bessel equation on the quantum calculus |
| topic | Bessel function modified Bessel function Bessel difference equation h-calculus the h-derivative and h-fractional function |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/541 |
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