Several identities involving the falling and rising factorials and the Cauchy, Lah, and Stirling numbers-Reference-Cited by-同舟云学术

Several identities involving the falling and rising factorials and the Cauchy, Lah, and Stirling numbers

Published:2016-12-01 Issue:2 Volume:8 Page:282-297
ISSN:2066-7752
Container-title:Acta Universitatis Sapientiae, Mathematica
language:en
Short-container-title:

Author:

Qi Feng¹,Shi Xiao-Ting²,Liu Fang-Fang²

Affiliation:

1. Institute of Mathematics, Henan Polytechnic University, China ; College of Mathematics, Inner Mongolia University for Nationalities, China ; Department of Mathematics, College of Science, Tianjin Polytechnic University, China

2. Department of Mathematics, College of Science, Tianjin Polytechnic University, China

Abstract

Abstract In the paper, the authors find several identities, including a new recurrence relation for the Stirling numbers of the first kind, involving the falling and rising factorials and the Cauchy, Lah, and Stirling numbers.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference42 articles.

1. [1] M. Abramowitz and I. A. Stegun (Eds), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series 55, 10th printing, Dover Publications, New York and Washington, 1972.

2. [2] Á. Besenyei, On complete monotonicity of some functions related to means, Math. Inequal. Appl. 16 (2013), no. 1, 233–239; Available online at http://dx.doi.org/10.7153/mia-16-17.

3. [3] N. Bourbaki, Functions of a Real Variable—Elementary Theory, Translated from the 1976 French original by Philip Spain. Elements of Mathematics (Berlin). Springer-Verlag, Berlin, 2004; Available online at http://dx.doi.org/10.1007/978-3-642-59315-4.

4. [4] L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, Revised and Enlarged Edition, D. Reidel Publishing Co., Dordrecht and Boston, 1974.

5. [5] B.-N. Guo and F. Qi, A completely monotonic function involving the trigamma function and with degree one, Appl. Math. Comput., 218 (2012), no. 19, 9890–9897; Available online at http://dx.doi.org/10.1016/j.amc.2012.03.075.

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