Decreasing property and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function

References

[1] ABRAMOWITZ, M. — STEGUN, I. A. (EDS.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series 55, Reprint of the 1972 edition, Dover Publications, Inc., New York, 1992.Suche in Google Scholar

[2] ALZER, H.: Complete monotonicity of a function related to the binomial probability, J. Math. Anal. Appl. 459(1) (2018), 10–15; available online at https://doi.org/10.1016/j.jmaa.2017.10.07710.1016/j.jmaa.2017.10.077Suche in Google Scholar

[3] BERG, C. — MASSA, E. — PERON, A. P.: A family of entire functions connecting the Bessel function J1 and the Lambert W function, Constr. Approx. 53(1) (2021), 121–154; available online at https://doi.org/10.1007/s00365-020-09499-x10.1007/s00365-020-09499-xSuche in Google Scholar

[4] GUO, B.-N. — QI, F.: Increasing property and logarithmic convexity of functions involving Riemann zeta function, arXiv (2022), available online at https://doi.org/10.48550/arXiv.2201.06970Suche in Google Scholar

[5] MITRINOVI´C, D. S. — PEˇCARI´C, J. E. — FINK, A. M.: Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht-Boston-London, 1993.Suche in Google Scholar

[6] QI, F.: Necessary and sufficient conditions for a difference defined by four derivatives of a function containing trigamma function to be completely monotonic, Appl. Comput. Math. 21(1) (2022), 61–70; available online at https://doi.org/10.30546/1683-6154.21.1.2022.6110.30546/1683-6154.21.1.2022.61Suche in Google Scholar

[7] QI, F.: Decreasing properties of two ratios defined by three and four polygamma functions, C. R. Math. Acad. Sci. Paris 360 (2022), 89–101; available online at https://doi.org/10.5802/crmath.29610.5802/crmath.296Suche in Google Scholar

[8] QI, F.: Lower bound of sectional curvature of Fisher–Rao manifold of beta distributions and complete monotonicity of functions involving polygamma functions, Results Math. 76(4) (2021), Art. No. 217, 16 pp.; available online at https://doi.org/10.1007/s00025-021-01530-210.1007/s00025-021-01530-2Suche in Google Scholar

[9] QI, F.: Monotonicity and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function, OSF Preprints (2020), available online at https://doi.org/10.31219/osf.io/whb2qSuche in Google Scholar

[10] QI, F.: Necessary and sufficient conditions for a difference constituted by four derivatives of a function involving trigamma function to be completely monotonic, Math. Inequal. Appl. 24(3) (2021), 845–855; available online at https://doi.org/10.7153/mia-2021-24-5810.7153/mia-2021-24-58Suche in Google Scholar

[11] QI, F.: Necessary and sufficient conditions for a ratio involving trigamma and tetragamma functions to be monotonic, Turkish J. Inequal. 5(1) (2021), 50–59.10.31219/osf.io/5rfb8Suche in Google Scholar

[12] QI, F.: Necessary and sufficient conditions for complete monotonicity and monotonicity of two functions defined by two derivatives of a function involving trigamma function, Appl. Anal. Discrete Math. 15(2) (2021), 378–392; available online at https://doi.org/10.2298/AADM191111014Q10.2298/AADM191111014QSuche in Google Scholar

[13] QI, F.: Two monotonic functions defined by two derivatives of a function involving trigamma function, TWMS J. Pure Appl. Math. 13(1) (2022), 91–104.Suche in Google Scholar

[14] QI, F.: Some properties of several functions involving polygamma functions and originating from the sectional curvature of the beta manifold, S˜ao Paulo J. Math. Sci. 14(2) (2020), 614–630; available online at https://doi.org/10.1007/s40863-020-00193-110.1007/s40863-020-00193-1Suche in Google Scholar

[15] QI, F. — GUO, B.-N.: From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions, J. Math. Anal. Appl. 493(1) (2021), Art. ID 124478, 19 pp.; available online at https://doi.org/10.1016/j.jmaa.2020.12447810.1016/j.jmaa.2020.124478Suche in Google Scholar PubMed PubMed Central

[16] QI, F. — HAN, L.-X. — YIN, H.-P.: Monotonicity and complete monotonicity of two functions defined by three derivatives of a function involving trigamma function, HAL preprint (2020), available online at https://hal.archives-ouvertes.fr/hal-0299820310.31219/osf.io/whb2qSuche in Google Scholar

[17] LIM, D. — QI, F.: Increasing property and logarithmic convexity of two functions involving Dirichlet eta function, J. Math. Inequal. 16(2) (2022), 463–469; available online at https://doi.org/10.7153/jmi-2022-16-3310.7153/jmi-2022-16-33Suche in Google Scholar

[18] QI, F. — LI, W.-H. — YU, S.-B. — DU, X.-Y. — GUO, B.-N.: A ratio of finitely many gamma functions and its properties with applications, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Math. RACSAM. 115(2) (2021), Art. No. 39, 14 pp.; available online at https://doi.org/10.1007/s13398-020-00988-z10.1007/s13398-020-00988-zSuche in Google Scholar

[19] QI, F. — NIU, D.-W. — LIM, D. — GUO, B.-N.: Some logarithmically completely monotonic functions and inequalities for multinomial coefficients and multivariate beta functions, Appl. Anal. Discrete Math. 14(2) (2020), 512–527; available online at https://doi.org/10.2298/AADM191111033Q10.2298/AADM191111033QSuche in Google Scholar

[20] SALEM, A. — ALZAHRANI, F.: Complete monotonicity property for two functions related to the q-digamma function, J.Math. Inequal. 13(1) (2019), 37–52; available online at https://doi.org/10.7153/jmi-2019-13-0310.7153/jmi-2019-13-03Suche in Google Scholar

[21] SCHILLING, R. L. — SONG, R. — VONDRAˇCEK, Z.: Bernstein Functions, 2nd ed., de Gruyter Studies in Mathematics 37, Walter de Gruyter, Berlin, Germany, 2012; available online at https://doi.org/10.1515/978311026933810.1515/9783110269338Suche in Google Scholar

[22] TIAN, J.-F. — YANG, Z.-H.: Asymptotic expansions of Gurland’s ratio and sharp bounds for their remainders, J. Math. Anal. Appl. 493(2) (2021), Art. ID 124545, 19 pp.; available online at https://doi.org/10.1016/j.jmaa.2020.12454510.1016/j.jmaa.2020.124545Suche in Google Scholar

[23] WANG, X.-F. — ISMAIL, M. E. H. — BATIR, N. — GUO, S.: A necessary and sufficient condition for sequences to be minimal completely monotonic, Adv. Difference Equ. 2020, Art. No. 665, 6 pp.; available online at https://doi.org/10.1186/s13662-020-03051-810.1186/s13662-020-03051-8Suche in Google Scholar

[24] WIDDER, D. V.: The Laplace Transform, Princeton University Press, Princeton, 1946.Suche in Google Scholar

[25] XU, A.-M. — CEN, Z.-D.: Qi’s conjectures on completely monotonic degrees of remainders of asymptotic formulas of di- and tri-gamma functions, J. Inequal. Appl. 2020, Art. No. 83, 10 pp.; available online at https://doi.org/10.1186/s13660-020-02345-510.1186/s13660-020-02345-5Suche in Google Scholar

[26] YANG, Z.-H. — TIAN, J.-F.: A class of completely mixed monotonic functions involving the gamma function with applications, Proc. Amer. Math. Soc. 146(11) (2018), 4707–4721; available online at https://doi.org/10.1090/proc/1419910.1090/proc/14199Suche in Google Scholar

[27] YANG, Z.-H. — TIAN, J.-F.: Monotonicity and inequalities for the gamma function, J. Inequal. Appl. 2017, Art. No. 317, 15 pp.; available online at https://doi.org/10.1186/s13660-017-1591-910.1186/s13660-017-1591-9Suche in Google Scholar

[28] YANG, Z.-H. — TIAN, J.-F.: Monotonicity rules for the ratio of two Laplace transforms with applications, J. Math. Anal. Appl. 470(2) (2019), 821–845; available online at https://doi.org/10.1016/j.jmaa.2018.10.03410.1016/j.jmaa.2018.10.034Suche in Google Scholar

[29] YANG, Z.-H. — TIAN, J.-F. — HA, M.-H.: A new asymptotic expansion of a ratio of two gamma functions and complete monotonicity for its remainder, Proc. Amer. Math. Soc. 148(5) (2020), 2163–2178; available online at https://doi.org/10.1090/proc/1491710.1090/proc/14917Suche in Google Scholar