On a conjecture of Chen-Guo-Wang

Preprint English OPEN
Ning, Bo; Zheng, Yu;
  • Subject: Mathematics - Combinatorics | Mathematics - Classical Analysis and ODEs | 05A20, 11B68

Towards confirming Sun's conjecture on the strict log-concavity of combinatorial sequence involving the n$th$ Bernoulli number, Chen, Guo and Wang proposed a conjecture about the log-concavity of the function $\theta(x)=\sqrt[x]{2\zeta(x)\Gamma(x+1)}$ for $x\in (6,\inft... View more
  • References (12)
    12 references, page 1 of 2

    [1] H. Alzer, On some inequalities for the gamma and psi functions, Math. Comp. 66 (1997), 373-389.

    [2] G.E. Andrews, R. Askey, R. Roy, Special Function, ISBN 7-302-09089-0.

    [3] W.Y.C. Chen, J.J.F. Guo, L.X.W. Wang, Infinitely log-monotonic combinatorial sequence, Adv. in Appl. Math. 52 (2014), 99-120.

    [4] W.Y.C. Chen, J.J.F. Guo, L.X.W. Wang, Zeta functions and the Log-behavior of combinatorial sequences, Proc. Edinb. Math. Soc. 58 (2015), 637-651.

    [5] Q.-H. Hou, Z.-W. Sun, H.-M. Wen, On monotonicity of some combinatorial sequences, Publ. Math. Debrecen, 85 (2014), no. 3-4, 285-295.

    [6] F. Luca, P. Sta˘nic˘a, On some conjectures on the monotonicity of some combinatorial sequences, J. Combin. Number Theory 4 (2012) 1-10.

    [7] P. Ribenboim, The Little Book of Bigger Primes, Second Edition, Springer-Verlag, New York, 2004.

    [8] Z.-W. Sun, Conjectures involving arithmetical sequences, Numbers Theory: Arithmetic in Shangri-La (eds., S. Kanemitsu, H. Li and J. Liu), Proc. 6th China-Japan Seminar (Shang-hai, August 15-17, 2011), World Sci., Singapore, 2013, pp. 244-258.

    [9] Y. Wang, B.-X. Zhu, Proofs of some conjectures on monotonicity of numbertheoretic and combinatorial sequences, Sci. China Math. 57 (11) (2014), 2429-2435.

    [10] E.X.W. Xia, O.X.M. Yao, A criterion for the log-convexity of combinatorial sequences, Electron. J. Combin. 20 (2013), no. 4, Paper 3, 10 pp.

  • Metrics
Share - Bookmark