A closed-form expression of a remarkable sequence of polynomials originating from a family of entire functions connecting the Bessel and Lambert functions
Tóm tắt
Từ khóa
Tài liệu tham khảo
Alzer, H., Berg, C.: Some classes of completely monotonic functions. Ann. Acad. Sci. Fenn. Math. 27(2), 445–460 (2002)
Berg, C.: Integral representation of some functions related to the gamma function. Mediterr. J. Math. 1(4), 433–439 (2004). https://doi.org/10.1007/s00009-004-0022-6
Berg, C., Massa, E., Peron, A.P.: A family of entire functions connecting the Bessel function $$J_1$$ and the Lambert $$W$$ function. Constr. Approx. 53(1), 121–154 (2021). https://doi.org/10.1007/s00365-020-09499-x
Chen, C.-P., Qi, F., Srivastava, H.M.: Some properties of functions related to the gamma and psi functions. Integral Transforms Spec. Funct. 21(2), 153–164 (2010). https://doi.org/10.1080/10652460903064216
Comtet, L.: Advanced Combinatorics: The Art of Finite and Infinite Expansions. Revised and Enlarged Edition, D. Reidel Publishing Co., Dordrecht and Boston, (1974). available online at https://doi.org/10.1007/978-94-010-2196-8
Guo, B.-N., Qi, F.: A property of logarithmically absolutely monotonic functions and the logarithmically complete monotonicity of a power-exponential function. Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 72(2), 21–30 (2010)
Olver, F.W.J., Lozier, D.W., Boisvert, R.F., Clark, C.W. (eds.), NIST Handbook of Mathematical Functions. Cambridge University Press, New York (2010). available online at http://dlmf.nist.gov/
Qi, F.: Diagonal recurrence relations for the Stirling numbers of the first kind. Contrib. Discrete Math. 11(1), 22–30 (2016). https://doi.org/10.11575/cdm.v11i1.62389
Qi, F.: Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind. Filomat 28(2), 319–327 (2014). https://doi.org/10.2298/FIL1402319O
Qi, F.: Some inequalities and an application of exponential polynomials. Math. Inequal. Appl. 23(1), 123–135 (2020). https://doi.org/10.7153/mia-2020-23-10
Qi, F., Agarwal, R.P.: On complete monotonicity for several classes of functions related to ratios of gamma functions. J. Inequal. Appl. 1, 1–42 (2019). https://doi.org/10.1186/s13660-019-1976-z
Qi, F., Chen, C.-P.: A complete monotonicity property of the gamma function. J. Math. Anal. Appl. 296(2), 603–607 (2004). https://doi.org/10.1016/j.jmaa.2004.04.026
Qi, F., Guo, B.-N.: A diagonal recurrence relation for the Stirling numbers of the first kind. Appl. Anal. Discrete Math. 12(1), 153–165 (2018). https://doi.org/10.2298/AADM170405004Q
Qi, F., Guo, B.-N.: Complete monotonicities of functions involving the gamma and digamma functions. RGMIA Res. Rep. Coll. 7(1), 63–72 (2004)
Qi, F., Li, W., Guo, B.-N.: Generalizations of a theorem of I. Schur. Appl. Math. E-Notes 6, 244–250 (2006)
Qi, F., Li, W.-H.: A logarithmically completely monotonic function involving the ratio of gamma functions. J. Appl. Anal. Comput. 5(4), 626–634 (2015). https://doi.org/10.11948/2015049
Qi, F., Niu, D.-W., Lim, D., Guo, B.-N.: Some properties and an application of multivariate exponential polynomials. Math. Methods Appl. Sci. 43(6), 2967–2983 (2020). https://doi.org/10.1002/mma.6095
Qi, F., Niu, D.-W., Lim, D., Yao, Y.-H.: Special values of the Bell polynomials of the second kind for some sequences and functions. J. Math. Anal. Appl. 491(2), 31 (2020). https://doi.org/10.1016/j.jmaa.2020.124382
Schilling, R.L., Song, R., Vondraček, Z.: Bernstein Functions. 2nd ed., de Gruyter Studies in Mathematics. Walter de Gruyter, Berlin, Germany (2012).
Widder, D.V.: The Laplace Transform. Princeton University Press, Princeton (1946)
