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Khan, Waseem Ahmad; Alatawi, Maryam Salem; Duran, Ugur

Applications and properties for bivariate Bell-based Frobenius-type Eulerian polynomials. (English) Zbl 1524.11055

J. Funct. Spaces 2023, Article ID 5205867, 10 p. (2023).

Cited in 1 Document

MSC:

11B68 Bernoulli and Euler numbers and polynomials

Keywords:

Frobenius-type Eulerian polynomials
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References:

[1] Jamei, M. M.; Beyki, M. R.; Koepf, W., A new type of Euler polynomials and numbers, Mediterranean Journal of Mathematics, 15, 3, 1-17 (2018) · Zbl 1422.11051 · doi:10.1007/s00009-018-1181-1
[2] Kim, T.; Ryoo, C. S., Some identities for Euler and Bernoulli polynomials and their zeros, Axioms, 7, 3, 56 (2018) · Zbl 1432.11021 · doi:10.3390/axioms7030056
[3] Kim, D. S.; Kim, T.; Lee, H., A note on degenerate Euler and Bernoulli polynomials of complex variable, Symmetry, 11, 9, 1168 (2019) · doi:10.3390/sym11091168
[4] Muhiuddin, G.; Khan, W. A.; Al-Kadi, D., Construction on the degenerate poly-Frobenius-Euler polynomials of complex variable, Journal of Function Spaces, 2021 (2021) · Zbl 1475.30021 · doi:10.1155/2021/3115424
[5] Kim, D. S.; Kim, T.; Kim, W. J.; Dolgy, D. V., A note on Eulerian polynomials, Abstract and Applied Analysis, 2012 (2012) · Zbl 1253.11026 · doi:10.1155/2012/269640
[6] Khan, W. A.; Srivastava, D., Certain properties of Apostol-type Hermite-based Frobenius-Genocchi polynomials, Kragujevac Journal of Mathematics, 45, 6, 859-872 (2021) · Zbl 1499.11106 · doi:10.46793/KgJMat2106.859K
[7] Srivastava, H. M.; Boutiche, M. A.; Rahmani, M., A class of Frobenius-type Eulerian polynomials, The Rocky Mountain Journal of Mathematics, 48, 1003-1013 (2018) · Zbl 1431.11036 · doi:10.1216/rmj-2018-48-3-1003
[8] Carlitz, L., Eulerian numbers and polynomials, Mathematics Magazine, 32, 5, 247-260 (1959) · Zbl 0092.06601 · doi:10.2307/3029225
[9] Carlitz, L., Eulerian numbers and polynomials of higher order, Duke Mathematical Journal, 27, 3, 401-423 (1960) · Zbl 0104.29003 · doi:10.1215/S0012-7094-60-02739-3
[10] Khan, W. A.; Nisar, K. S.; Mehmet, A.; Duran, U., A novel kind of Hermite-based Frobenius type Eulerian polynomials, Proceedings of the Jangjeon Mathematical Society, 22, 4, 551-563 (2019) · Zbl 1447.11038
[11] Khan, W. A.; Srivastava, D., On the generalized Apostol-type Frobenius-Genocchi polynomials, Filomat Journal, 33, 7, 1967-1977 (2019) · Zbl 1499.11107 · doi:10.2298/FIL1907967K
[12] Ashraf, A. U.; Tran, T. N.; Yoshinaga, M., Eulerian polynomials for subarrangements of Weyl arrangements, Advances in Applied Mathematic, 120, article 102064 (2020) · Zbl 1447.52026 · doi:10.1016/j.aam.2020.102064
[13] Duran, U.; Mehmet, A.; Araci, S., Bell-based Bernoulli polynomials with applications, Axioms, 10, 1, 29 (2021) · doi:10.3390/axioms10010029
[14] Khan, W. A.; Muhiuddin, G.; Muhyi, A.; Al-Kadi, D., Analytical properties of type 2 degenerate poly-Bernoulli polynomials associated with their applications, Advances in Difference Equations, 2021, 1 (2021) · Zbl 1494.11018 · doi:10.1186/s13662-021-03575-7
[15] Ryoo, C. S.; Khan, W. A., On two bivariate kinds of poly-Bernoulli and poly-Genocchi polynomials, Mathematics, 8, 3, 417 (2020) · doi:10.3390/math8030417
[16] Pathan, M. A.; Khan, W. A., A new class of generalized Apostol-type Frobenius-Euler-Hermite polynomials, Honam Mathematical Journal, 42, 3, 477-499 (2020) · Zbl 1476.11057
[17] Mezö, I., A new formula for the Bernoulli polynomials, Results in Mathematics, 58, 3-4, 329-335 (2010) · Zbl 1237.11010 · doi:10.1007/s00025-010-0039-z
[18] Kim, D. S.; Kim, T., Some identities of degenerate Bell polynomials, Mathematics, 8, 1, 40 (2020) · doi:10.3390/math8010040
[19] Border, A. Z., The r-Stirling numbers, Discrete Mathematics, 49, 3, 241-259 (1984) · Zbl 0535.05006 · doi:10.1016/0012-365X(84)90161-4
[20] Pathan, M. A.; Khan, W. A., On λ-Changhee-Hermite polynomials, Analysis, 42, 2, 57-69 (2022) · Zbl 1487.11029 · doi:10.1515/anly-2021-1012
[21] Bell, E. T., Exponential polynomials, The Annals of Mathematics, 35, 2, 258-277 (1934) · JFM 60.0295.01 · doi:10.2307/1968431
[22] Khan, W. A.; Kamarujjama, M.; Daud, Construction of partially degenerate Bell-Bernoulli polynomials of the first kind and their certain properties, Analysis, 42, 3, 171-184 (2022) · Zbl 1506.11036 · doi:10.1515/anly-2021-1028
[23] Alam, N.; Khan, W. A.; Ryoo, C. S., A note on Bell-based Apostol-type Frobenius-Euler polynomials of complex variable with its certain applications, Mathematics, 10, 12, 2109 (2022) · doi:10.3390/math10122109
[24] Alam, N.; Khan, W. A.; Obeidat, S.; Muhiuddin, G.; Diab, N. S.; Ziadi, H. N.; Altaleb, A.; Bachioua, L., A note on Bell-based Bernoulli and Euler polynomials of complex variable, Computer Modeling in Engineering and Sciences, 135, 1, 187-209 (2023) · doi:10.32604/cmes.2022.021418
[25] Corcino, R. B.; Corcino, C. B.; Ontolan, J. M.; Perez, C. M.; Cantallopez, E. R., Hankel transform of q-noncentral Bell numbers, International Journal of Mathematics and Mathematical Sciences, 2015 (2015) · Zbl 1393.11021 · doi:10.1155/2015/417327
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