Several closed expressions for the Euler numbers
Tóm tắt
Từ khóa
Tài liệu tham khảo
Abramowitz, M, Stegun, IA (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 10th edn. Applied Mathematics Series, vol. 55. National Bureau of Standards, Washington (1972)
Temme, NM: Special Functions: An Introduction to Classical Functions of Mathematical Physics. A Wiley-Interscience Publication. Wiley, New York (1996). doi: 10.1002/9781118032572
Brent, RP, Harvey, D: Fast computation of Bernoulli, tangent and secant numbers. In: Computational and Analytical Mathematics. Springer Proc. Math. Stat., vol. 50, pp. 127-142. Springer, New York (2013). doi: 10.1007/978-1-4614-7621-4_8
Guo, B-N, Qi, F: Explicit formulae for computing Euler polynomials in terms of Stirling numbers of the second kind. J. Comput. Appl. Math. 272, 251-257 (2014). doi: 10.1016/j.cam.2014.05.018
Guo, B-N, Qi, F: Explicit formulas for special values of the Bell polynomials of the second kind and the Euler numbers. ResearchGate Technical Report (2015). doi: 10.13140/2.1.3794.8808
Kim, DS, Kim, T, Kim, YH, Lee, SH: Some arithmetic properties of Bernoulli and Euler numbers. Adv. Stud. Contemp. Math. (Kyungshang) 22(4), 467-480 (2012)
Qi, F: Derivatives of tangent function and tangent numbers. Appl. Math. Comput. (2015, in press). arXiv:1202.1205v3
Malenfant, J: Finite, closed-form expressions for the partition function and for Euler, Bernoulli, and Stirling numbers (2011). arXiv:1103.1585
Vella, DC: Explicit formulas for Bernoulli and Euler numbers. Integers 8, A01 (2008)
Yakubovich, S: Certain identities, connection and explicit formulas for the Bernoulli, Euler numbers and Riemann zeta-values (2014). arXiv:1406.5345
Bourbaki, N: Functions of a Real Variable, Elementary Theory: Elements of Mathematics. Springer, Berlin (2004). doi: 10.1007/978-3-642-59315-4 ; Translated from the 1976 French original by Philip Spain.
Comtet, L: Advanced Combinatorics: The Art of Finite and Infinite Expansions, revised and enlarged edition. Reidel, Dordrecht (1974)
Qi, F, Zheng, M-M: Explicit expressions for a family of the Bell polynomials and applications. Appl. Math. Comput. 258, 597-607 (2015). doi: 10.1016/j.amc.2015.02.027
Qi, F, Wei, C-F: Several closed expressions for the Euler numbers. ResearchGate Technical Report (2015). doi: 10.13140/2.1.3474.7688