# Some paperspublished by Feng Qi in 2019

1. Feng Qi and Bai-Ni Guo, Viewing some ordinary differential equations from the angle of derivative polynomials, Iranian Journal of Mathematical Sciences and Informatics 14 (2019), no. 2, in press.
2. Jian Sun, Bo-Yan Xi, and Feng Qi, Some new inequalities of the Hermite–Hadamard type for extended $s$-convex functions, Journal of Computational Analysis and Applications 26 (2019), no. 6, 985–996.
3. Jun Zhang, Zhi-Li Pei, and Feng Qi, Integral inequalities of Simpson’s type for strongly extended $(s,m)$-convex functions, Journal of Computational Analysis and Applications 26 (2019), no. 3, 499–508.

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## Part One: Formally published papers in 2018

1. Feng Qi, A simple form for coefficients in a family of nonlinear ordinary differential equations, Advances and Applications in Mathematical Sciences 17 (2018), in press.
2. Feng Qi, An improper integral, the beta function, the Wallis ratio, and the Catalan numbers, Problemy Analiza–Issues of Analysis 7 (25) (2018), in press; Available online at https://doi.org/10.15393/j3.art.2018.????.
3. Feng Qi, Integral representations for multivariate logarithmic polynomials, Journal of Computational and Applied Mathematics 336 (2018), 54–62; Available online at https://doi.org/10.1016/j.cam.2017.11.047.
4. Feng Qi, Notes on several families of differential equations related to the generating function for the Bernoulli numbers of the second kind, Turkish Journal of Analysis and Number Theory 6 (2018), no. 2, 40–42; Available online at https://doi.org/10.12691/tjant-6-2-1.
5. Feng Qi, On multivariate logarithmic polynomials and their properties, Indagationes Mathematicae 29 (2018), in press; Available online at https://doi.org/10.1016/j.indag.2018.04.002.
6. Feng Qi, Simple forms for coefficients in two families of ordinary differential equations, Global Journal of Mathematical Analysis 6 (2018), no. 1, 7–9; Available online at https://doi.org/10.14419/gjma.v6i1.9778.
7. Feng Qi, Simplifying coefficients in a family of nonlinear ordinary differential equations, Acta et Commentationes Universitatis Tartuensis de Mathematica (2018), in press.
8. Feng Qi, Abdullah Akkurt, and Hüseyin Yildirim, Catalan numbers, $k$-gamma and $k$-beta functions, and parametric integrals, Journal of Computational Analysis and Applications 25 (2018), no. 6, 1036–1042.
9. Feng Qi, Ravi Bhukya, and Venkatalakshmi Akavaram, Inequalities of the Grünbaum type for completely monotonic functions, Advances and Applications in Mathematical Sciences 17 (2018), no. 3, 331–339.
10. Feng Qi, Viera Čerňanová, Xiao-Ting Shi, and Bai-Ni Guo, Some properties of central Delannoy numbers, Journal of Computational and Applied Mathematics 328 (2018), 101–115; Available online at https://doi.org/10.1016/j.cam.2017.07.013.
11. Feng Qi and Bai-Ni Guo, A diagonal recurrence relation for the Stirling numbers of the first kind, Applicable Analysis and Discrete Mathematics 12 (2018), no. 1, 153–165; Available online at https://doi.org/10.2298/AADM170405004Q.
12. Feng Qi and Bai-Ni Guo, Lévy–Khintchine representation of Toader–Qi mean, Mathematical Inequalities & Applications 21 (2018), no. 2, 421–431; Available online at https://doi.org/10.7153/mia-2018-21-29.
13. Feng Qi and Bai-Ni Guo, On the sum of the Lah numbers and zeros of the Kummer confluent hypergeometric function, Acta Universitatis Sapientiae Mathematica 10 (2018), no. 1, in press.
14. Feng Qi and Bai-Ni Guo, Some properties and generalizations of the Catalan, Fuss, and Fuss–Catalan numbers, Chapter 5 in Mathematical Analysis and Applications: Selected Topics, First Edition, 101–133; Edited by Michael Ruzhansky, Hemen Dutta, and Ravi P. Agarwal; Published 2018 by John Wiley & Sons, Inc.; Available online at https://doi.org/10.1002/9781119414421.ch5.
15. Feng Qi and Bai-Ni Guo, The reciprocal of the weighted geometric mean is a Stieltjes function, Boletín de la Sociedad Matemática Mexicana, Tercera Serie 24 (2018), no. 1, 181–202; Available online at http://dx.doi.org/10.1007/s40590-016-0151-5.
16. Feng Qi and Bai-Ni Guo, The reciprocal of the weighted geometric mean of many positive numbers is a Stieltjes function, Quaestiones Mathematicae 41 (2018), in press; Available online at https://doi.org/10.2989/16073606.2017.1396508.
17. Feng Qi and Dongkyu Lim, Integral representations of bivariate complex geometric mean and their applications, Journal of Computational and Applied Mathematics 330 (2018), 41–58; Available online at http://dx.doi.org/10.1016/j.cam.2017.08.005.
18. Feng Qi, Dongkyu Lim, and Bai-Ni Guo, Explicit formulas and identities for the Bell polynomials and a sequence of polynomials applied to differential equations, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales-Serie A: Matemáticas 112 (2018), in press; Available online at http://dx.doi.org/10.1007/s13398-017-0427-2.
19. Feng Qi, Cristinel Mortici, and Bai-Ni Guo, Some properties of a sequence arising from geometric probability for pairs of hyperplanes intersecting with a convex body, Computational & Applied Mathematics 37 (2018), no. 2, 2190–2200; Available online at http://dx.doi.org/10.1007/s40314-017-0448-7.
20. Feng Qi and Kottakkaran Sooppy Nisar, Some integral transforms of the generalized $k$-Mittag-Leffler function, Publications de l’Institut Mathématique (Beograd) 103 (117) (2018), in press.
21. Feng Qi, Da-Wei Niu, and Bai-Ni Guo, Some identities for a sequence of unnamed polynomials connected with the Bell polynomials, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales-Serie A: Matemáticas 112 (2018), in press; Available online at https://doi.org/10.1007/s13398-018-0494-z.
22. Feng Qi, Xiao-Ting Shi, and Bai-Ni Guo, Integral representations of the large and little Schröder numbers, Indian Journal of Pure and Applied Mathematics 49 (2018), no. 1, 23–38; Available online at https://doi.org/10.1007/s13226-018-0258-7.
23. Feng Qi, Xiao-Ting Shi, and Fang-Fang Liu, An integral representation, complete monotonicity, and inequalities of the Catalan numbers, Filomat (2018), in press.
24. Feng Qi, Jing-Lin Wang, and Bai-Ni Guo, A representation for derangement numbers in terms of a tridiagonal determinant, Kragujevac Journal of Mathematics 42 (2018), no. 1, 7–14.
25. Feng Qi, Jing-Lin Wang, and Bai-Ni Guo, Notes on a family of inhomogeneous linear ordinary differential equations, Advances and Applications in Mathematical Sciences 17 (2018), no. 4, 361–368.
26. Feng Qi, Jing-Lin Wang, and Bai-Ni Guo, Simplifying differential equations concerning degenerate Bernoulli and Euler numbers, Transactions of A. Razmadze Mathematical Institute 172 (2018), no. 1, 90–94; Available online at http://dx.doi.org/10.1016/j.trmi.2017.08.001.
27. Feng Qi and Jiao-Lian Zhao, Some properties of the Bernoulli numbers of the second kind and their generating function, Bulletin of the Korean Mathematical Society 55 (2018), in press; Available online at https://doi.org/10.4134/BKMS.2018.55.?.???. (WOS:???)
28. Feng Qi, Jiao-Lian Zhao, and Bai-Ni Guo, Closed forms for derangement numbers in terms of the Hessenberg determinants, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales-Serie A: Matemáticas 112 (2018), in press; Available online at http://dx.doi.org/10.1007/s13398-017-0401-z.
29. Kottakkaran Sooppy Nisar, Feng Qi, Gauhar Rahman, Shahid Mubeen, and Muhammad Arshad, Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric $k$-function, Journal of Inequalities and Applications 2018, in press; Available online at https://doi.org/10.1186/s13660-018-1717-8.
30. Li Yin and Feng Qi, Some functional inequalities for generalized error function, Journal of Computational Analysis and Applications 25 (2018), no. 7, 1366–1372.
31. Bo-Yan Xi, Shu-Ping Bai, and Feng Qi, On integral inequalities of the Hermite–Hadamard type for co-ordinated $(\alpha,m_1)$-$(s,m_2)$-convex functions, Journal of Interdisciplinary Mathematics 21 (2018), in press.
32. Hong-Ping Yin, Jing-Yu Wang, and Feng Qi, Some integral inequalities of Hermite–Hadamard type for $s$-geometrically convex functions, Miskolc Mathematical Notes (2018), in press.

## Part Two: Preprints in 2018

1. Feng Qi, A logarithmically completely monotonic function involving the $q$-gamma function, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01796696.
2. Feng Qi and Bai-Ni Guo, An alternative proof for complete monotonicity of linear combinations of many psi functions, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01773131.
3. Feng Qi, Dongkyu Lim, and Ai-Qi Liu, Explicit expressions related to degenerate Cauchy numbers and their generating function, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01725045.
4. Feng Qi, Dongkyu Lim, and Yong-Hong Yao, Notes on two kinds of special values for the Bell polynomials of the second kind, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01757740.
5. Feng Qi and Ai-Qi Liu, Notes on complete monotonicity related to the difference of the psi and logarithmic functions, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01728682.
6. Feng Qi, Da-Wei Niu, and Dongkyu Lim, Notes on the Rodrigues formulas for two kinds of the Chebyshev polynomials, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01705040.
7. Feng Qi, Da-Wei Niu, Dongkyu Lim, and Bai-Ni Guo, Explicit formulas and identities on Bell polynomials and falling factorials, ResearchGate Preprint (2018), available online at https://doi.org/10.13140/RG.2.2.34679.52640.
8. Feng Qi, Da-Wei Niu, Dongkyu Lim, and Bai-Ni Guo, Some logarithmically completely monotonic functions and inequalities for multinomial coefficients and multivariate beta functions, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01769288.
9. Feng Qi, Da-Wei Niu, Dongkyu Lim, and Bai-Ni Guo, Some properties and an application of multivariate exponential polynomials, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01745173.
10. Feng Qi, Da-Wei Niu, Dongkyu Lim, and Yong-Hong Yao, Special values of the Bell polynomials of the second kind for some sequences and functions, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01766566.
11. Feng Qi, Gauhar Rahman, and Kottakkaran Sooppy Nisar, Convexity and inequalities related to extended beta and confluent hypergeometric functions, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01703900.
12. Feng Qi, Shao-Wen Yao, and Bai-Ni Guo, A class of integral means and the modified Bessel functions of the first kind, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01796905.
13. Kottakkaran Sooppy Nisar, Feng Qi, Gauhar Rahman, Shahid Mubeen, and Muhammad Arshad, Some inequalities involving the extended gamma and beta functions, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01701647.
14. Gauhar Rahman, Feng Qi, Kottakkaran Sooppy Nisar, and Abdul Ghaffar, Some inequalities of the Hermite–Hadamard type concerning $k$-fractional conformable integrals, ResearchGate Preprint (2018), available online at https://doi.org/10.13140/RG.2.2.16226.63686.
15. Ravi Bhukya, Venkatalakshmi Akavaram, and Feng Qi, Some inequalities of the Turán type for confluent hypergeometric functions of the second kind, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01701854.
16. Bo-Yan Xi, Dan-Dan Gao, and Feng Qi, Integral inequalities of Hermite–Hadamard type for $(\alpha,s)$-convex and $(\alpha,s,m)$-convex functions, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01761678.
17. Siddra Habib, Shahid Mubeen, Muhammad Nawaz Naeem, and Feng Qi, Generalized $k$-fractional conformable integrals and related inequalities, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01788916.

# Some papers on $q$-analogues of the gamma and polygamma functions

1. Feng Qi, A completely monotonic function related to the $q$-trigamma function, University Politehnica of Bucharest Scientific Bulletin Series A—Applied Mathematics and Physics 76 (2014), no. 1, 107–114.
2. Feng Qi, A logarithmically completely monotonic function involving the $q$-gamma function, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01796696.
3. Feng Qi, Bounds for the ratio of two gamma functions, Journal of Inequalities and Applications 2010, Article ID 493058, 84 pages; Available online at https://doi.org/10.1155/2010/493058.
4. Feng Qi, Bounds for the ratio of two gamma functions: from Gautschi’s and Kershaw’s inequalities to complete monotonicity, Turkish Journal of Analysis and Number Theory 2 (2014), no. 5, 152–164; Available online at https://doi.org/10.12691/tjant-2-5-1.
5. Feng Qi, Certain logarithmically $N$-alternating monotonic functions involving gamma and $q$-gamma functions, Nonlinear Functional Analysis and Applications 12 (2007), no. 4, 675–685.
6. Feng Qi, Complete monotonicity of functions involving the $q$-trigamma and $q$-tetragamma functions, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales–Serie A: Matemáticas 109 (2015), no. 2, 419–429; Available online at https://doi.org/10.1007/s13398-014-0193-3.
7. Feng Qi and Bai-Ni Guo, Complete monotonicity of divided differences of the di- and tri-gamma functions with applications, Georgian Mathematical Journal 23 (2016), no. 2, 279–291; Available online at https://doi.org/10.1515/gmj-2016-0004.
8. Feng Qi, Fang-Fang Liu, and Xiao-Ting Shi, Comments on two completely monotonic functions involving the $q$-trigamma function, Journal of Inequalities and Special Functions 7 (2016), no. 4, 211–217.
9. Feng Qi and Qiu-Ming Luo, Bounds for the ratio of two gamma functions—From Wendel’s and related inequalities to logarithmically completely monotonic functions, Banach Journal of Mathematical Analysis 6 (2012), no. 2, 132–158; Available online at https://doi.org/10.15352/bjma/1342210165.
10. Bai-Ni Guo and Feng Qi, Properties and applications of a function involving exponential functions, Communications on Pure and Applied Analysis 8 (2009), no. 4, 1231–1249; Available online at https://doi.org/10.3934/cpaa.2009.8.1231.

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# Some papers related to the function $e^{1/x}$ and the Lah numbers

1. Xiao-Jing Zhang, Feng Qi, and Wen-Hui Li, Properties of three functions relating to the exponential function and the existence of partitions of unity, International Journal of Open Problems in Computer Science and Mathematics 5 (2012), no. 3, 122–127; Available online at https://doi.org/10.12816/0006128.
2. Siad Daboul, Jan Mangaldan, Michael Z. Spivey, Peter J. Taylor, The Lah numbers and the $n$th derivative of $e^{1/x}$, Mathematics Magazine 86 (2013), no. 1, 39–47; Available online at https://doi.org/10.4169/math.mag.86.1.039.
3. Khristo N. Boyadzhiev, Lah numbers, Laguerre polynomials of order negative one, and the $n$th derivative of $\exp(1/x)$, Acta Universitatis Sapientiae Mathematica 8 (2016), no. 1, 22–31; Available online at https://doi.org/10.1515/ausm-2016-0002.
4. Jacob Katriel, The $q$-Lah numbers and the $n$-th $q$-derivative of $\exp_q(1/x)$, Notes on Number Theory and Discrete Mathematics 23 (2017), no. 2, 45–47.
5. Feng Qi, An explicit formula for the Bell numbers in terms of the Lah and Stirling numbers, Mediterranean Journal of Mathematics 13 (2016), no. 5, 2795–2800; Available online at https://doi.org/10.1007/s00009-015-0655-7.
6. Feng Qi, Derivatives of tangent function and tangent numbers, Applied Mathematics and Computation 268 (2015), 844–858; Available online at https://doi.org/10.1016/j.amc.2015.06.123.
7. Feng Qi, Diagonal recurrence relations for the Stirling numbers of the first kind, Contributions to Discrete Mathematics 11 (2016), no. 1, 22–30; Available online at http://hdl.handle.net/10515/sy5wh2dx6 and https://doi.org/10515/sy5wh2dx6.
8. Feng Qi, Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind, Filomat 28 (2014), no. 2, 319–327; Available online at https://doi.org/10.2298/FIL1402319O.
9. Feng Qi, Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions, Mathematical Inequalities & Applications 18 (2015), no. 2, 493–518; Available online at https://doi.org/10.7153/mia-18-37.
10. Feng Qi and Christian Berg, Complete monotonicity of a difference between the exponential and trigamma functions and properties related to a modified Bessel function, Mediterranean Journal of Mathematics 10 (2013), no. 4, 1685–1696; Available online at https://doi.org/10.1007/s00009-013-0272-2.
11. Feng Qi and Bai-Ni Guo, On the sum of the Lah numbers and zeros of the Kummer confluent hypergeometric function, Acta Universitatis Sapientiae Mathematica 10 (2018), no. 1, in press.
12. Feng Qi, Dongkyu Lim, and Bai-Ni Guo, Explicit formulas and identities for the Bell polynomials and a sequence of polynomials applied to differential equations, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales–Serie A: Matemáticas 112 (2018), in press; Available online at https://doi.org/10.1007/s13398-017-0427-2.
13. Feng Qi and Shu-Hong Wang, Complete monotonicity, completely monotonic degree, integral representations, and an inequality related to the exponential, trigamma, and modified Bessel functions, Global Journal of Mathematical Analysis 2 (2014), no. 3, 91–97; Available online at https://doi.org/10.14419/gjma.v2i3.2919.
14. Feng Qi and Miao-Miao Zheng, Explicit expressions for a family of the Bell polynomials and applications, Applied Mathematics and Computation 258 (2015), 597–607; Available online at https://doi.org/10.1016/j.amc.2015.02.027.
15. Bai-Ni Guo and Feng Qi, Six proofs for an identity of the Lah numbers, Online Journal of Analytic Combinatorics 10 (2015), 5 pages.
16. Bai-Ni Guo and Feng Qi, Some integral representations and properties of Lah numbers, Journal for Algebra and Number Theory Academia 4 (2014), no. 3, 77–87.
17. Chun-Fu Wei and Bai-Ni Guo, Complete monotonicity of functions connected with the exponential function and derivatives, Abstract and Applied Analysis 2014, Art. ID 851213, 5 pp. Available online at https://doi.org/10.1155/2014/851213.