A Note on Higher Order Degenerate Changhee–Genocchi Numbers and Polynomials of the Second Kind
In this paper, we consider the higher order degenerate Changhee–Genocchi polynomials of the second kind by using generating functions and the Riordan matrix methods. At the same time, we give some properties of the higher order degenerate Changhee–Genocchi polynomials of the second kind. In addition...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-12-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/15/1/56 |
| _version_ | 1797436896338509824 |
|---|---|
| author | Liwei Liu Wuyungaowa |
| author_facet | Liwei Liu Wuyungaowa |
| author_sort | Liwei Liu |
| collection | DOAJ |
| description | In this paper, we consider the higher order degenerate Changhee–Genocchi polynomials of the second kind by using generating functions and the Riordan matrix methods. At the same time, we give some properties of the higher order degenerate Changhee–Genocchi polynomials of the second kind. In addition, we establish some new equalities involving the higher order degenerate Changhee–Genocchi polynomials of the second kind, the generalized Bell polynomials, higher order Changhee polynomials, the higher order degenerate Daehee polynomials of the second kind, Lah numbers and Stirling numbers, etc. |
| first_indexed | 2024-03-09T11:08:17Z |
| format | Article |
| id | doaj.art-8db2e299f5994ba1af57893b839b62fc |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T11:08:17Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-8db2e299f5994ba1af57893b839b62fc2023-12-01T00:51:06ZengMDPI AGSymmetry2073-89942022-12-011515610.3390/sym15010056A Note on Higher Order Degenerate Changhee–Genocchi Numbers and Polynomials of the Second KindLiwei Liu0Wuyungaowa1Department of Mathematics, Inner Mongolia University, Huhhot 010020, ChinaDepartment of Mathematics, Inner Mongolia University, Huhhot 010020, ChinaIn this paper, we consider the higher order degenerate Changhee–Genocchi polynomials of the second kind by using generating functions and the Riordan matrix methods. At the same time, we give some properties of the higher order degenerate Changhee–Genocchi polynomials of the second kind. In addition, we establish some new equalities involving the higher order degenerate Changhee–Genocchi polynomials of the second kind, the generalized Bell polynomials, higher order Changhee polynomials, the higher order degenerate Daehee polynomials of the second kind, Lah numbers and Stirling numbers, etc.https://www.mdpi.com/2073-8994/15/1/56the higher order degenerate Euler polynomialsthe higher orderdegenerate Genocchi polynomialsthe higher order degenerate Changhee polynomials of the second kindthe higher orderdegenerate Daehee polynomials of the second kindStirling numbersLah numbers |
| spellingShingle | Liwei Liu Wuyungaowa A Note on Higher Order Degenerate Changhee–Genocchi Numbers and Polynomials of the Second Kind Symmetry the higher order degenerate Euler polynomials the higher orderdegenerate Genocchi polynomials the higher order degenerate Changhee polynomials of the second kind the higher orderdegenerate Daehee polynomials of the second kind Stirling numbers Lah numbers |
| title | A Note on Higher Order Degenerate Changhee–Genocchi Numbers and Polynomials of the Second Kind |
| title_full | A Note on Higher Order Degenerate Changhee–Genocchi Numbers and Polynomials of the Second Kind |
| title_fullStr | A Note on Higher Order Degenerate Changhee–Genocchi Numbers and Polynomials of the Second Kind |
| title_full_unstemmed | A Note on Higher Order Degenerate Changhee–Genocchi Numbers and Polynomials of the Second Kind |
| title_short | A Note on Higher Order Degenerate Changhee–Genocchi Numbers and Polynomials of the Second Kind |
| title_sort | note on higher order degenerate changhee genocchi numbers and polynomials of the second kind |
| topic | the higher order degenerate Euler polynomials the higher orderdegenerate Genocchi polynomials the higher order degenerate Changhee polynomials of the second kind the higher orderdegenerate Daehee polynomials of the second kind Stirling numbers Lah numbers |
| url | https://www.mdpi.com/2073-8994/15/1/56 |
| work_keys_str_mv | AT liweiliu anoteonhigherorderdegeneratechangheegenocchinumbersandpolynomialsofthesecondkind AT wuyungaowa anoteonhigherorderdegeneratechangheegenocchinumbersandpolynomialsofthesecondkind AT liweiliu noteonhigherorderdegeneratechangheegenocchinumbersandpolynomialsofthesecondkind AT wuyungaowa noteonhigherorderdegeneratechangheegenocchinumbersandpolynomialsofthesecondkind |