[PDF] Top 20 Note on a Class of Completely Monotonic Functions Involving the Polygamma Functions

... [1] M. Abramowitz and I. A. Stegun (Eds), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Reprint of the 1972 edition. A Wiley-Interscience Pub- lication. Selected Government ... See full document

... pletely monotonic function” was introduced explicitly in [9], published formally in [8], and used immediately in [2, 4, 10, 11, ...logarithmically completely monotonic functions on (0, ∞) can ... See full document

... studying completely monotonic functions is the connection between infinitely divisible probability distributions (measure) on R and [0, ∞) and completely monotonic functions ... See full document

... also note that the logarithmically complete monotonicity of ratios of two gamma functions is closely related to the divided difference of psi and polygamma ... See full document

... Yang, Zh.-H., Tian, J.-F.: A class of completely mixed monotonic functions involving the gamma function with applications.. Zhang, S.-Q., Qi, F.: Some integral inequalities.[r] ... See full document

... the completely monotonic or logarithmically completely monotonic func- tions have been the subject of intensive ...and polygamma function can be found in the literature ... See full document

... of functions involving Euler’s gamma function and originating from certain problems of traffic flow are proved to be logarithmically completely monotonic and a class of functions ... See full document

... inequality involving the Wallis’ function about the Euler’s gamma function is ...tions involving the divided differences of the psi function ψ and polygamma function ψ 0 are ... See full document

... a class of functions involving the Euler’s gamma function are proved, a class of the first Kershaw type double inequalities are established, and the first Kershaw’s double inequality and ... See full document

... A class of logarithmically completely monotonic functions and application to the best bounds in the second Gautschi-Kershaw’s inequality, ... See full document

... conditions that a class of functions involving ratio of gamma functions are logarithmically completely monotonic , RGMIA Res. Chen, The best bounds in Gautschi-Kershaw inequalities , Mat[r] ... See full document

... [4] F. Guo, Complete monotonicities of functions involving the gamma and digamma functions, RGMIA Res. Available online at http://rgmia. Qi) Department of Applied Mathematics and Informa[r] ... See full document

... Zhao, T.-H., Chu, Y.-M.: A class of logarithmically completely monotonic functions associated with a gamma function.. Zhao, T.-H., Chu, Y.-M., Jiang, Y.-P.: Monotonic and logarithmically[r] ... See full document

... the completely monotonic or logarithmically completely monotonic func- tions have been the subject of intensive ...monotonicity involving the gamma, psi and polygamma ... See full document

... Abstract. A function involving the divided differences of the psi function and the polygamma functions is proved to be completely monotonic. As an appli- cation of this result, the ... See full document

... inequality involving a positive linear operator acting on the composition of two continuous functions is presented and, as applications of this inequality, some new inequalities involving the beta, ... See full document

... A class of logarithmically completely monotonic functions and application to the best bounds in the second Gautschi-Kershaw’s inequality, ... See full document

... alternating monotonic functions are established and the monotonicity results of some functions involving the gamma and q-gamma functions, which are ob- tained in ...Inequalities ... See full document

... logarithmically completely monotonic functions on I is denoted by ...logarithmically completely monotonic functions on (0, ∞) can be characterized as the infinitely divisible ... See full document

... logarithmically completely monotonic on an interval I if f has derivatives of all orders on I and its logarithm ln f satisfies (–) n (ln f (x)) (n) ≥  for all n ∈ N on I (see ...the completely ... See full document