November  2009, 8(6): 1975-1989. doi: 10.3934/cpaa.2009.8.1975

Completely monotonic functions involving divided differences of the di- and tri-gamma functions and some applications

1. 

College of Mathematics and Information Science, Henan Normal University, Xinxiang City, Henan Province, 453007, China

2. 

School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010

Received  October 2008 Revised  April 2009 Published  August 2009

In the present paper, we establish the complete monotonicity of two functions involving divided differences of the digamma function $\psi$ and the trigamma function $\psi'$. Applying these monotonicity, we provide an alternative proof for the monotonicity and convexity of a function derived from bounding the ratio of two gamma functions, procure the logarithmically completely monotonic property of a function involving the ratio of two gamma functions, and obtain new bounds for the ratio of two gamma functions.
Citation: Feng Qi, Bai-Ni Guo. Completely monotonic functions involving divided differences of the di- and tri-gamma functions and some applications. Communications on Pure and Applied Analysis, 2009, 8 (6) : 1975-1989. doi: 10.3934/cpaa.2009.8.1975
[1]

Michal Málek, Peter Raith. Stability of the distribution function for piecewise monotonic maps on the interval. Discrete and Continuous Dynamical Systems, 2018, 38 (5) : 2527-2539. doi: 10.3934/dcds.2018105

[2]

H. W. Broer, K. Saleh, V. Naudot, R. Roussarie. Dynamics of a predator-prey model with non-monotonic response function. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 221-251. doi: 10.3934/dcds.2007.18.221

[3]

Yulin Zhao. On the monotonicity of the period function of a quadratic system. Discrete and Continuous Dynamical Systems, 2005, 13 (3) : 795-810. doi: 10.3934/dcds.2005.13.795

[4]

Johan Matheus Tuwankotta, Eric Harjanto. Strange attractors in a predator–prey system with non-monotonic response function and periodic perturbation. Journal of Computational Dynamics, 2019, 6 (2) : 469-483. doi: 10.3934/jcd.2019024

[5]

Bai-Ni Guo, Feng Qi. Properties and applications of a function involving exponential functions. Communications on Pure and Applied Analysis, 2009, 8 (4) : 1231-1249. doi: 10.3934/cpaa.2009.8.1231

[6]

Francesco Mainardi. On some properties of the Mittag-Leffler function $\mathbf{E_\alpha(-t^\alpha)}$, completely monotone for $\mathbf{t> 0}$ with $\mathbf{0<\alpha<1}$. Discrete and Continuous Dynamical Systems - B, 2014, 19 (7) : 2267-2278. doi: 10.3934/dcdsb.2014.19.2267

[7]

Yuri Latushkin, Alim Sukhtayev. The Evans function and the Weyl-Titchmarsh function. Discrete and Continuous Dynamical Systems - S, 2012, 5 (5) : 939-970. doi: 10.3934/dcdss.2012.5.939

[8]

J. William Hoffman. Remarks on the zeta function of a graph. Conference Publications, 2003, 2003 (Special) : 413-422. doi: 10.3934/proc.2003.2003.413

[9]

H. N. Mhaskar, T. Poggio. Function approximation by deep networks. Communications on Pure and Applied Analysis, 2020, 19 (8) : 4085-4095. doi: 10.3934/cpaa.2020181

[10]

Hassan Emamirad, Philippe Rogeon. Semiclassical limit of Husimi function. Discrete and Continuous Dynamical Systems - S, 2013, 6 (3) : 669-676. doi: 10.3934/dcdss.2013.6.669

[11]

Ken Ono. Parity of the partition function. Electronic Research Announcements, 1995, 1: 35-42.

[12]

Tomasz Downarowicz, Yonatan Gutman, Dawid Huczek. Rank as a function of measure. Discrete and Continuous Dynamical Systems, 2014, 34 (7) : 2741-2750. doi: 10.3934/dcds.2014.34.2741

[13]

Peter Giesl. Construction of a global Lyapunov function using radial basis functions with a single operator. Discrete and Continuous Dynamical Systems - B, 2007, 7 (1) : 101-124. doi: 10.3934/dcdsb.2007.7.101

[14]

Josef Diblík, Zdeněk Svoboda. Asymptotic properties of delayed matrix exponential functions via Lambert function. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 123-144. doi: 10.3934/dcdsb.2018008

[15]

Jeremy Levesley, Xinping Sun, Fahd Jarad, Alexander Kushpel. Interpolation of exponential-type functions on a uniform grid by shifts of a basis function. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2399-2416. doi: 10.3934/dcdss.2020403

[16]

Lv Chen, Hailiang Yang. Optimal reinsurance and investment strategy with two piece utility function. Journal of Industrial and Management Optimization, 2017, 13 (2) : 737-755. doi: 10.3934/jimo.2016044

[17]

Giovanni Colombo, Khai T. Nguyen. On the minimum time function around the origin. Mathematical Control and Related Fields, 2013, 3 (1) : 51-82. doi: 10.3934/mcrf.2013.3.51

[18]

Welington Cordeiro, Manfred Denker, Michiko Yuri. A note on specification for iterated function systems. Discrete and Continuous Dynamical Systems - B, 2015, 20 (10) : 3475-3485. doi: 10.3934/dcdsb.2015.20.3475

[19]

Luc Robbiano. Counting function for interior transmission eigenvalues. Mathematical Control and Related Fields, 2016, 6 (1) : 167-183. doi: 10.3934/mcrf.2016.6.167

[20]

Todd Kapitula, Björn Sandstede. Eigenvalues and resonances using the Evans function. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : 857-869. doi: 10.3934/dcds.2004.10.857

2021 Impact Factor: 1.273

Metrics

  • PDF downloads (178)
  • HTML views (0)
  • Cited by (20)

Other articles
by authors

[Back to Top]