A three-term recurrence formula for the generalized Bernoulli polynomials
DOI :
https://doi.org/10.5269/bspm.41705Résumé
In the present paper, we propose some new explicit formulas of the higher order Daehee polynomials in terms of the generalized r-Stirling and r-Whitney numbers of the second kind. As a consequence, we derive a three-term recurrence formula for the calculation of the generalized Bernoulli polynomials of order k.
Références
1. M. A. Boutiche, M. Rahmani and H. M. Srivastava, Explicit formulas associated with some families of generalized Bernoulli and Euler polynomials, Mediterr. J. Math. 14, Art. 89, 10, (2017).
2. A. Z. Broder, The r-Stirling numbers, Discrete Math. 49, 241–259, (1984).
3. L. Carlitz, Weighted Stirling numbers of the first and second kind. I, Fibonacci Quart. 18, 147–162, (1980).
4. L. Carlitz, Weighted Stirling numbers of the first and second kind. II, Fibonacci Quart. 18, 242–257, (1980).
5. D. S. Kim, T. Kim, S. H. Lee and J. J. Seo, Higher-order Daehee numbers and polynomials, Int. J. Math. Anal. 8, 273–283, (2014).
6. I. Mezo, A new formula for the Bernoulli polynomials, Results Math. 58, 329–335, (2010).
7. M. Rahmani, Generalized Stirling transform, Miskolc Math. Notes 15, 677–690, (2014).
8. M. Rahmani, Some results on Whitney numbers of Dowling lattices, Arab J. Math. Sci. 20, 11–27, (2014).
9. M. Rahmani, On p-Bernoulli numbers and polynomials, J. Number Theory 157, 350–366, (2015).
2. A. Z. Broder, The r-Stirling numbers, Discrete Math. 49, 241–259, (1984).
3. L. Carlitz, Weighted Stirling numbers of the first and second kind. I, Fibonacci Quart. 18, 147–162, (1980).
4. L. Carlitz, Weighted Stirling numbers of the first and second kind. II, Fibonacci Quart. 18, 242–257, (1980).
5. D. S. Kim, T. Kim, S. H. Lee and J. J. Seo, Higher-order Daehee numbers and polynomials, Int. J. Math. Anal. 8, 273–283, (2014).
6. I. Mezo, A new formula for the Bernoulli polynomials, Results Math. 58, 329–335, (2010).
7. M. Rahmani, Generalized Stirling transform, Miskolc Math. Notes 15, 677–690, (2014).
8. M. Rahmani, Some results on Whitney numbers of Dowling lattices, Arab J. Math. Sci. 20, 11–27, (2014).
9. M. Rahmani, On p-Bernoulli numbers and polynomials, J. Number Theory 157, 350–366, (2015).
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Publié
2020-10-11
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Research Articles
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