Some papers published in 2018 by Feng Qi

Some papers published in 2018 by Feng Qi

Part One: Formally Published Papers in 2018

  1. 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.
  2. 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.
  3. 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), in press; Available online at https://doi.org/10.2298/AADM170405004Q.
  4. Feng Qi and Bai-Ni Guo, Lévy–Khintchine representation of Toader–Qi mean, Mathematical Inequalities & Applications 21 (2018), in press.
  5. 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.
  6. 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, 35 pages, edited by H. Dutta, M. Ruzhansky, and R. P. Agarwal, Wiley, October 2018. (ISBN 9781119414346)
  7. 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), in press; Available online at http://dx.doi.org/10.1007/s40590-016-0151-5.
  8. 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.
  9. 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.
  10. 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.
  11. 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), in press; Available online at http://dx.doi.org/10.1007/s40314-017-0448-7.
  12. Feng Qi, B. Ravi, and A. Venkat Lakshmi, Inequalities of the Grünbaum type for completely monotonic functions, Advances and Applications in Mathematical Sciences 17 (2018), in press.
  13. 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), in press.
  14. 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.
  15. 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 (2018), in press.
  16. 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), in press; Available online at http://dx.doi.org/10.1016/j.trmi.2017.08.001.
  17. 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.
  18. Kottakkaran Sooppy Nisar and Feng Qi, Some integral transforms of the generalized $k$-Mittag-Leffler function, Publications de l’Institut Mathématique (Beograd) 103(117) (2018), in press.
  19. Li Yin and Feng Qi, Some functional inequalities for generalized error function, Journal of Computational Analysis and Applications 25 (2018), no. 7, 1366–1372.
  20. 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.

Part Two: Preprints in 2018

  1. in progress.
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Some papers published in 2017 by Feng Qi

Some papers published in 2017 by Feng Qi

Part One: Formally Published Papers in 2017

  1. Feng Qi, Bounding the difference and ratio between the weighted arithmetic and geometric means, International Journal of Analysis and Applications 13 (2017), no. 2, 132–135.
  2. Feng Qi, Parametric integrals, the Catalan numbers, and the beta function, Elemente der Mathematik 72 (2017), no. 3, 103–110; Available online at http://dx.doi.org/10.4171/EM/332.
  3. Feng Qi, Some inequalities for the Bell numbers, Proceedings of the Indian Academy of Sciences (Mathematical Sciences) 127 (2017), no. 4, 551–564; Available online at http://dx.doi.org/10.1007/s12044-017-0355-2.
  4. Feng Qi, Serkan Araci, and Mehmet Acıkgöz, On an analogue of Euler polynomials and related to extended fermionic $p$-adic integrals on $\mathbb{Z}_p$, Iranian Journal of Science and Technology, Transaction A: Science 41 (2017), no. 3, 613–618; Available online at https://doi.org/10.1007/s40995-017-0274-1.
  5. Feng Qi and Jacques Gélinas, Revisiting Bouvier’s paper on tangent numbers, Advances and Applications in Mathematical Sciences 16 (2017), no. 8, 275–281.
  6. Feng Qi and Bai-Ni Guo, A closed form for the Stirling polynomials in terms of the Stirling numbers, Tbilisi Mathematical Journal 10 (2017), no. 4, 153–158; Available online at https://doi.org/10.1515/tmj-2017-0053.
  7. Feng Qi and Bai-Ni Guo, A criterion to justify a holomorphic function, Global Journal of Mathematical Analysis 5 (2017), no. 1, 24–26; Available online at http://dx.doi.org/10.14419/gjma.v5i1.7398.
  8. Feng Qi and Bai-Ni Guo, A determinantal expression and a recurrence relation for the Euler polynomials, Advances and Applications in Mathematical Sciences 16 (2017), no. 9, 297–309.
  9. Feng Qi and Bai-Ni Guo, Alternative proofs for summation formulas of some trigonometric series, Global Journal of Mathematical Analysis 5 (2017), no. 2, 44–46; Available online at http://dx.doi.org/10.14419/gjma.v5i2.7471.
  10. Feng Qi and Bai-Ni Guo, An explicit formula for derivative polynomials of the tangent function, Acta Universitatis Sapientiae Mathematica 9 (2017), no. 2, in press; Available online at http://dx.doi.org/10.1515/ausm-2017-????.
  11. Feng Qi and Bai-Ni Guo, Explicit and recursive formulas, integral representations, and properties of the large Schröder numbers, Kragujevac Journal of Mathematics 41 (2017), no. 1, 121–141.
  12. Feng Qi and Bai-Ni Guo, Explicit formulas and recurrence relations for higher order Eulerian polynomials, Indagationes Mathematicae 28 (2017), no. 4, 884–891; Available online at https://doi.org/10.1016/j.indag.2017.06.010.
  13. Feng Qi and Bai-Ni Guo, Explicit formulas for special values of the Bell polynomials of the second kind and for the Euler numbers and polynomials, Mediterranean Journal of Mathematics 14 (2017), no. 3, Article 140, 14 pages; Available online at http://dx.doi.org/10.1007/s00009-017-0939-1.
  14. Feng Qi and Bai-Ni Guo, Expressing the generalized Fibonacci polynomials in terms of a tridiagonal determinant, Le Matematiche 72 (2017), no. 1, 167–175; Available online at http://dx.doi.org/10.4418/2017.72.1.13.
  15. Feng Qi and Bai-Ni Guo, Integral representations and complete monotonicity of remainders of the Binet and Stirling formulas for the gamma function, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales-Serie A: Matemáticas 111 (2017), no. 2, 425–434; Available online at http://dx.doi.org/10.1007/s13398-016-0302-6.
  16. Feng Qi and Bai-Ni Guo, Integral representations of the Catalan numbers and their applications, Mathematics 5 (2017), no. 3, Article 40, 31 pages; Available online at http://dx.doi.org/10.3390/math5030040.
  17. Feng Qi and Bai-Ni Guo, Some explicit and recursive formulas of the large and little Schröder numbers, Arab Journal of Mathematical Sciences 23 (2017), no. 2, 141–147; Available online at http://dx.doi.org/10.1016/j.ajmsc.2016.06.002.
  18. Feng Qi and Bai-Ni Guo, Some properties of the average numbers of comparisons used by the quicksort, Journal of Mathematical Analysis 8 (2017), no. 2, 123–128.
  19. Feng Qi and Bai-Ni Guo, The reciprocal of the geometric mean of many positive numbers is a Stieltjes transform, Journal of Computational and Applied Mathematics 311 (2017), 165–170; Available online at http://dx.doi.org/10.1016/j.cam.2016.07.006.
  20. Feng Qi and Bai-Ni Guo, Two nice determinantal expressions and a recurrence relation for the Apostol–Bernoulli polynomials, Journal of the Indonesian Mathematical Society 23 (2017), no. 1, 81–87; Available online at http://dx.doi.org/10.22342/jims.23.1.274.81-87.
  21. Feng Qi and Mansour Mahmoud, Bounding the gamma function in terms of the trigonometric and exponential functions, Acta Scientiarum Mathematicarum 83 (2017), no. 1-2, 125–141; Available online at http://dx.doi.org/10.14232/actasm-016-813-x.
  22. Feng Qi, Xiao-Ting Shi, and Fang-Fang Liu, Expansions of the exponential and the logarithm of power series and applications, Arabian Journal of Mathematics (2017), no. 2, 95–108; Available online at http://dx.doi.org/10.1007/s40065-017-0166-4.
  23. Feng Qi, Xiao-Ting Shi, Fang-Fang Liu, and Dmitry V. Kruchinin, Several formulas for special values of the Bell polynomials of the second kind and applications, Journal of Applied Analysis and Computation 7 (2017), no. 3, 857–871; Available online at http://dx.doi.org/10.11948/2017054.
  24. Feng Qi, Xiao-Ting Shi, Fang-Fang Liu, and Zhen-Hang Yang, A double inequality for an integral mean in terms of the exponential and logarithmic means, Periodica Mathematica Hungarica 75 (2017), no. 2, 180–189; Available online at http://dx.doi.org/10.1007/s10998-016-0181-9.
  25. Feng Qi, Xiao-Ting Shi, Mansour Mahmoud, and Fang-Fang Liu, The Catalan numbers: a generalization, an exponential representation, and some properties, Journal of Computational Analysis and Applications 23 (2017), no. 5, 937–944.
  26. Feng Qi, Xiao-Jing Zhang, and Wen-Hui Li, The harmonic and geometric means are Bernstein functions, Boletín de la Sociedad Matemática Mexicana, Tercera Serie 23 (2017), no. 2, 713–736; Available online at http://dx.doi.org/10.1007/s40590-016-0085-y.
  27. Praveen Agarwal, Feng Qi, Mehar Chand, and Shilpi Jain, Certain integrals involving the generalized hypergeometric function and the Laguerre polynomials, Journal of Computational and Applied Mathematics 313 (2017), 307–317; Available online at http://dx.doi.org/10.1016/j.cam.2016.09.034.
  28. Kottakkaran Sooppy Nisar and Feng Qi, On solutions of fractional kinetic equations involving the generalized $k$-Bessel function, Note di Matematica (2017), in press.
  29. Ye Shuang and Feng Qi, Integral inequalities of the Hermite–Hadamard type for $(\alpha,m)$-GA-convex functions, Journal of Nonlinear Sciences and Applications 10 (2017), no. 4, 1854–1860; Available online at http://dx.doi.org/10.22436/jnsa.010.04.45.
  30. Shu-Hong Wang and Feng Qi, Hermite–Hadamard type inequalities for $s$-convex functions via Riemann-Liouville fractional integrals, Journal of Computational Analysis and Applications 22 (2017), no. 6, 1124–1134.
  31. Jiao-Lian Zhao and Feng Qi, Two explicit formulas for the generalized Motzkin numbers, Journal of Inequalities and Applications 2017, 2017:44, 8 pages; Available online at http://dx.doi.org/10.1186/s13660-017-1313-3.
  32. Jun Zhang, Zhi-Li Pei, and Feng Qi, Some integral inequalities of Hermite–Hadamard type for $\varepsilon$-convex functions, Turkish Journal of Analysis and Number Theory 5 (2017), no. 3, 117–120; Available online at http://dx.doi.org/10.12691/tjant-5-3-5.
  33. Jiao-Lian Zhao, Jing-Lin Wang, and Feng Qi, Derivative polynomials of a function related to the Apostol–Euler and Frobenius–Euler numbers, Journal of Nonlinear Sciences and Applications 10 (2017), no. 4, 1345–1349; Available online at http://dx.doi.org/10.22436/jnsa.010.04.06.
  34. Chun-Ying He, Yan Wang, Bo-Yan Xi, and Feng Qi, Hermite-Hadamard type inequalities for $(\alpha,m)$-HA and strongly $(\alpha,m)$-GA convex functions, Journal of Nonlinear Sciences and Applications 10 (2017), no. 1, 205–214; Available online at http://dx.doi.org/10.22436/jnsa.010.01.20.
  35. Jun Zhang, Zhi-Li Pei, Gao-Chao Xu, Xiao-Hui Zhou, and Feng Qi, Integral inequalities of extended Simpson type for $(\alpha,m)$-$\varepsilon$-convex functions, Journal of Nonlinear Sciences and Applications 10 (2017), no. 1, 122–129; Available online at http://dx.doi.org/10.22436/jnsa.010.01.12.

Part Two: Preprints in 2017

  1. Feng Qi, A double inequality for the ratio of two consecutive Bernoulli numbers, Preprints 2017, 2017080099, 7 pages; Available online at https://doi.org/10.20944/preprints201708.0099.v1.
  2. Feng Qi, Integral representations for multivariate logarithmic polynomials, Preprints 2017, 2017090112, 11 pages; Available online at https://doi.org/10.20944/preprints201709.0112.v1.
  3. Feng Qi, Notes on several families of differential equations related to the generating function for the Bernoulli numbers of the second kind, ResearchGate Preprint (2017), available online at https://doi.org/10.13140/RG.2.2.13291.23843.
  4. Feng Qi, On multi-order logarithmic polynomials and their explicit formulas, recurrence relations, and inequalities, Preprints 2017, 2017090034, 11 pages; Available online at https://doi.org/10.20944/preprints201709.0034.v1.
  5. Feng Qi, Some inequalities of the Bell polynomials, Preprints 2017, 2017080079, 10 pages; Available online at https://doi.org/10.20944/preprints201708.0079.v1 and https://doi.org/10.20944/preprints201708.0079.v2.
  6. Feng Qi, Some properties of the Touchard polynomials, ResearchGate Working Paper (2017), available online at https://doi.org/10.13140/RG.2.2.30022.16967.
  7. 祁锋,与第二类Chebyshev多项式和Catalan数相关的一个矩阵之逆和几个恒等式,ResearchGate Presentation (2017), available online at https://doi.org/10.13140/RG.2.2.22832.46081/1.
  8. Feng Qi, Abdullah Akkurt, and Hüseyin Yildirim, Catalan numbers, $k$-gamma and $k$-beta functions, and parametric integrals, ResearchGate Working Paper (2017), available online at http://dx.doi.org/10.13140/RG.2.2.19398.06721.
  9. Feng Qi and Pietro Cerone, Some properties of the Fuss–Catalan numbers, Preprints 2017, 2017080056, 14 pages; Available online at http://dx.doi.org/10.20944/preprints201708.0056.v1.
  10. Feng Qi and Jacques Gélinas, Revisiting Bouvier’s paper on tangent numbers, ResearchGate Working Paper (2017), available online at http://dx.doi.org/10.13140/RG.2.2.34641.74089.
  11. Feng Qi and Bai-Ni Guo, A closed form for the Stirling polynomials in terms of the Stirling numbers, Preprints 2017, 2017030055, 4 pages; Available online at http://dx.doi.org/10.20944/preprints201703.0055.v1.
  12. Feng Qi and Bai-Ni Guo, Expressing the generalized Fibonacci polynomials in terms of a tridiagonal determinant, ResearchGate Working Paper (2017), available online at http://dx.doi.org/10.13140/RG.2.2.32352.07680.
  13. Feng Qi and Bai-Ni Guo, Identities of the Chebyshev polynomials, the inverse of a triangular matrix, and identities of the Catalan numbers, Preprints 2017, 2017030209, 21 pages; Available online at http://dx.doi.org/10.20944/preprints201703.0209.v1.
  14. Feng Qi and Bai-Ni Guo, Integral representations of Catalan numbers and their applications, Preprints 2017, 2017040040, 34 pages; Available online at http://dx.doi.org/10.20944/preprints201704.0040.v1.
  15. Feng Qi and Bai-Ni Guo, Lévy–Khintchine representation of Toader–Qi mean, Preprints 2017, 2017030119, 10 pages; Available online at http://dx.doi.org/10.20944/preprints201703.0119.v1.
  16. Feng Qi and Bai-Ni Guo, Several explicit and recursive formulas for the generalized Motzkin numbers, Preprints 2017, 2017030200, 11 pages; Available online at http://dx.doi.org/10.20944/preprints201703.0200.v1.
  17. Feng Qi and Dongkyu Lim, Integral representations for bivariate complex geometric mean and applications, Preprints 2017, 2017050039, 24 pages; Available online at http://dx.doi.org/10.20944/preprints201705.0039.v1.
  18. Feng Qi, Dongkyu Lim, and Bai-Ni Guo, Some identities relating to Eulerian polynomials and involving Stirling numbers, Preprints 2017, 2017080004, 10 pages; Available online at http://dx.doi.org/10.20944/preprints201708.0004.v1.
  19. Feng Qi, Da-Wei Niu, and Bai-Ni Guo, Simplification of coefficients in differential equations associated with higher order Frobenius–Euler numbers, Preprints 2017, 2017080017, 7 pages; Available online at http://dx.doi.org/10.20944/preprints201708.0017.v1.
  20. Feng Qi, Da-Wei Niu, and Bai-Ni Guo, Simplifying coefficients in differential equations associated with higher order Bernoulli numbers of the second kind, Preprints 2017, 2017080026, 6 pages; Available online at http://dx.doi.org/10.20944/preprints201708.0026.v1.
  21. Feng Qi, Da-Wei Niu, and Bai-Ni Guo, Some identities for a sequence of unnamed polynomials connected with the Bell polynomials, Preprints 2017, 2017080044, 10 pages; Available online at http://dx.doi.org/10.20944/preprints201708.0044.v1.
  22. Feng Qi, Da-Wei Niu, Dongkyu Lim, and Bai-Ni Guo, Generalizations of the Bell numbers and polynomials and their properties, Preprints 2017, 2017080090, 12 pages; Available online at https://doi.org/10.20944/preprints201708.0090.v1.
  23. Feng Qi, Da-Wei Niu, Dongkyu Lim, and Bai-Ni Guo, A unified generalization of the Bell numbers and the Touchard polynomials and its properties, ResearchGate Working Paper (2017), available online at https://doi.org/10.13140/RG.2.2.36733.05603.
  24. Feng Qi, Xiao-Long Qin, and Yong-Hong Yao, The generating function of the Catalan numbers and lower triangular integer matrices, Preprints 2017, 2017110120, 12 pages; Available online at https://doi.org/10.20944/preprints201711.0120.v1.
  25. Feng Qi, Jing-Lin Wang, and Bai-Ni Guo, Closed expressions of the Fibonacci polynomials in terms of tridiagonal determinants, Preprints 2017, 2017030208, 10 pages; Available online at http://dx.doi.org/10.20944/preprints201703.0208.v1.
  26. Feng Qi, Jing-Lin Wang, and Bai-Ni Guo, Notes on a family of inhomogeneous linear ordinary differential equations, Preprints 2017, 2017040026, 5 pages; Available online at http://dx.doi.org/10.20944/preprints201704.0026.v1.
  27. Feng Qi, Jing-Lin Wang, and Bai-Ni Guo, Simplifying and finding nonlinear ordinary differential equations, ResearchGate Working Paper (2017), available online at http://dx.doi.org/10.13140/RG.2.2.28855.32166.
  28. Feng Qi, Jing-Lin Wang, and Bai-Ni Guo, Simplifying differential equations concerning degenerate Bernoulli and Euler numbers, ResearchGate Working Paper (2017), available online at http://dx.doi.org/10.13140/RG.2.2.12078.10566.
  29. Feng Qi, Jing-Lin Wang, and Bai-Ni Guo, Simplifying two families of nonlinear ordinary differential equations, Preprints 2017, 2017030192, 6 pages; Available online at http://dx.doi.org/10.20944/preprints201703.0192.v1.
  30. Feng Qi and Jiao-Lian Zhao, Some properties of the Bernoulli numbers of the second kind and their generating function, ResearchGate Working Paper (2017), available online at http://dx.doi.org/10.13140/RG.2.2.13058.27848.
  31. Feng Qi, Qing Zou, and Bai-Ni Guo, Identities of the Chebyshev polynomials, the inverse of a triangular matrix, and identities of the Catalan numbers, ResearchGate Working Paper (2017), available online at http://dx.doi.org/10.13140/RG.2.2.27344.71684.
  32. Feng Qi, Qing Zou, and Bai-Ni Guo, Some identities and a matrix inverse related to the Chebyshev polynomials of the second kind and the Catalan numbers, Preprints 2017, 2017030209, 25 pages; Available online at http://dx.doi.org/10.20944/preprints201703.0209.v2.
  33. Li Yin and Feng Qi, Several series identities involving the Catalan numbers, Preprints 2017, 2017030029, 11 pages; Available online at http://dx.doi.org/10.20944/preprints201703.0029.v1.
  34. Praveen Agarwal, Mohamed Jleli, and Feng Qi, Extended Weyl fractional integrals and their inequalities, arXiv preprint (2017), available online at https://arxiv.org/abs/1705.03131.
  35. Jiao-Lian Zhao, Jing-Lin Wang, and Feng Qi, Derivative polynomials of a function related to the Apostol–Euler and Frobenius–Euler numbers, ResearchGate Working Paper (2017), available online at http://dx.doi.org/10.13140/RG.2.2.35572.35204.

Related Links-相关链接

  1. Feng Qi, Some Papers Authored by Professor Dr. Feng Qi and Indexed by the Web of Science and the Engineering Village Since 1997, ResearchGate Technical Report.
  2. Feng Qi, The List of Papers and Preprints Authored by Professor Dr. Feng Qi Since 1993, ResearchGate Technical Report.

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Some papers published by Feng Qi on generating functions and ordinary differential equations

Some papers published by Feng Qi on generating functions and ordinary differential equations

  1. Feng Qi, Explicit formulas for the convolved Fibonacci numbers, ResearchGate Working Paper (2016), available online at https://doi.org/10.13140/RG.2.2.36768.17927.
  2. Feng Qi, Notes on several families of differential equations related to the generating function for the Bernoulli numbers of the second kind, ResearchGate Preprint (2017), available online at https://doi.org/10.13140/RG.2.2.13291.23843.
  3. 祁锋,与第二类Chebyshev多项式和Catalan数相关的一个矩阵之逆和几个恒等式, ResearchGate Presentation (2017), available online at https://doi.org/10.13140/RG.2.2.22832.46081/1.
  4. 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, in press; Available online at https://doi.org/10.2298/AADM170405004Q.
  5. Feng Qi and Bai-Ni Guo, Explicit formulas and recurrence relations for higher order Eulerian polynomials, Indagationes Mathematicae 28 (2017), no. 4, 884–891; Available online at https://doi.org/10.1016/j.indag.2017.06.010.
  6. Feng Qi and Bai-Ni Guo, Explicit formulas for derangement numbers and their generating function, Journal of Nonlinear Functional Analysis 2016, Article ID 45, 10 pages.
  7. Feng Qi and Bai-Ni Guo, Some properties of the Hermite polynomials and their squares and generating functions, Preprints 2016, 2016110145, 14 pages; Available online at https://doi.org/10.20944/preprints201611.0145.v1.
  8. Feng Qi and Bai-Ni Guo, Viewing some ordinary differential equations from the angle of derivative polynomials, Preprints 2016, 2016100043, 12 pages; Available online at https://doi.org/10.20944/preprints201610.0043.v1.
  9. 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, Fìsicas y Naturales–Serie A: Matemàticas 112 (2018), in press; Available online at https://doi.org/10.1007/s13398-017-0427-2.
  10. Feng Qi, Dongkyu Lim, and Bai-Ni Guo, Some identities relating to Eulerian polynomials and involving Stirling numbers, Preprints 2017, 2017080004, 10 pages; Available online at https://doi.org/10.20944/preprints201708.0004.v1.
  11. Feng Qi, Da-Wei Niu, and Bai-Ni Guo, Simplification of coefficients in differential equations associated with higher order Frobenius–Euler numbers, Preprints 2017, 2017080017, 7 pages; Available online at https://doi.org/10.20944/preprints201708.0017.v1.
  12. Feng Qi, Da-Wei Niu, and Bai-Ni Guo, Simplifying coefficients in differential equations associated with higher order Bernoulli numbers of the second kind, Preprints 2017, 2017080026, 6 pages; Available online at https://doi.org/10.20944/preprints201708.0026.v1.
  13. Feng Qi, Da-Wei Niu, and Bai-Ni Guo, Some identities for a sequence of unnamed polynomials connected with the Bell polynomials, Preprints 2017, 2017080044, 10 pages; Available online at https://doi.org/10.20944/preprints201708.0044.v1.
  14. Feng Qi, Xiao-Long Qin, and Yong-Hong Yao, The generating function of the Catalan numbers and lower triangular integer matrices, Preprints 2017, 2017110120, 12 pages; Available online at https://doi.org/10.20944/preprints201711.0120.v1.
  15. 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 (2018), in press.
  16. Feng Qi, Jing-Lin Wang, and Bai-Ni Guo, Simplifying and finding nonlinear ordinary differential equations, ResearchGate Working Paper (2017), available online at https://doi.org/10.13140/RG.2.2.28855.32166.
  17. Feng Qi, Jing-Lin Wang, and Bai-Ni Guo, Simplifying differential equations concerning degenerate Bernoulli and Euler numbers, ResearchGate Working Paper (2017), available online at https://doi.org/10.13140/RG.2.2.12078.10566.
  18. Feng Qi and Jiao-Lian Zhao, Some properties of the Bernoulli numbers of the second kind and their generating function, ResearchGate Working Paper (2017), available online at https://doi.org/10.13140/RG.2.2.13058.27848.
  19. Feng Qi, Qing Zou, and Bai-Ni Guo, Some identities and a matrix inverse related to the Chebyshev polynomials of the second kind and the Catalan numbers, Preprints 2017, 2017030209, 25 pages; Available online at https://doi.org/10.20944/preprints201703.0209.v2.
  20. Bai-Ni Guo and Feng Qi, Explicit formulae for computing Euler polynomials in terms of Stirling numbers of the second kind, Journal of Computational and Applied Mathematics 272 (2014), 251–257; Available online at https://doi.org/10.1016/j.cam.2014.05.018.
  21. Bai-Ni Guo and Feng Qi, Some identities and an explicit formula for Bernoulli and Stirling numbers, Journal of Computational and Applied Mathematics 255 (2014), 568–579; Available online at https://doi.org/10.1016/j.cam.2013.06.020.
  22. Jiao-Lian Zhao, Jing-Lin Wang, and Feng Qi, Derivative polynomials of a function related to the Apostol–Euler and Frobenius–Euler numbers, Journal of Nonlinear Sciences and Applications 10 (2017), no. 4, 1345–1349; Available online at https://doi.org/10.22436/jnsa.010.04.06.
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The reciprocal of the weighted geometric mean of many positive numbers is a Stieltjes function

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The reciprocal of the weighted geometric mean of many positive numbers is a Stieltjes function

Taylor & Francis Online

The online platform for Taylor & Francis Group content

Author Services | FAQ | Twitter | Facebook

Dear Feng Qi,

Congratulations! Your article, The reciprocal of the weighted geometric mean of many positive numbers is a Stieltjes function, has just been published on Taylor & Francis Online. We’d like to work with you to ensure your article reaches as many people as possible, and has the impact you want it to. To help with this, all authors receive 50 free eprints, a link you can share with colleagues and friends, giving them free access to your article.

Share your 50 free eprints today
Start using your eprints today by pasting the link below into emails, on your personal or departmental website, on social media, or even on your blog. Everyone who clicks on the link will be taken to your full article:

http://www.tandfonline.com/eprint/WqcZ2NVZdKqDHJufN5Gd/full

Twitter   Facebook   email

Your eprint link is for you to share in any way you like, and author feedback tells us it is a highly effective way to promote your research to your networks. The link will also continue to work after the free access allowance is reached, by directing people to the abstract page.

You can find eprint links to your other Taylor & Francis articles by going to your Authored Works on Taylor & Francis Online.

Working with us to highlight your article
We want to increase the impact of your article, and we work with authors to ensure your work reaches the widest possible (and most appropriate) audiences. Discover some simple yet effective ways to highlight your research.

Author exclusive: 30% off Routledge & CRC Press books
All authors who’ve had an article published in a Taylor & Francis Group journal receive a 30% discount on their book purchases with us. Find out how to claim your discount by visiting yourAuthored Works.

If you have any problems accessing your Taylor & Francis Online account, or using your eprints, please contact our dedicated support team at support@tandfonline.com.

Kind regards,

Author Services team

Interested in insights, tips, and updates for Taylor & Francis authors? Be part of our researcher community on:
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Facebook
Taylor & Francis Author Services

Taylor & Francis

7 ways you can highlight your article

  1. Share your eprint link with your networks.
  2. Talk about your research on social media.
  3. Add a link to your article on your email signature.
  4. Add your article to reading lists
  5. Post a link to your article on your profile on any professional or academic network you’re a member of.
  6. Put a link to your article on your institutional profile page, your personal webpage or any project websites.
  7. If you blog, why not blog about your article.

Find out more about how you can work with us tohighlight your research.

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