<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Department of Mathematics, College of Science, Tianjin Polytechnic University,

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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...

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

Published Online: Jan 23, 2017

Page range: 282 - 297

Received: Jun 12, 2016

DOI: https://doi.org/10.1515/ausm-2016-0019

Keywords
identity, Cauchy number, Lah number, Stirling number, falling factorial, rising factorial, Faà di Bruno formula

© 2016 Feng Qi et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Jan 23, 2017

Page range: 282 - 297

Received: Jun 12, 2016

DOI: https://doi.org/10.1515/ausm-2016-0019

Keywordsidentity, Cauchy number, Lah number, Stirling number, falling factorial, rising factorial, Faà di Bruno formula

© 2016 Feng Qi et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
identity, Cauchy number, Lah number, Stirling number, falling factorial, rising factorial, Faà di Bruno formula