Abstract
In this paper, we define Hurwitz–Lerch multi-poly-Cauchy numbers using the multiple polylogarithm factorial function. Furthermore, we establish properties of these types of numbers and obtain two different forms of the explicit formula using Stirling numbers of the first kind.
Highlights
The Cauchy numbers [1,2,3] of the first and second kind, respectively denoted by cn and ĉn, play important roles in many applications in number theory, combinatorics, and in different areas such as approximate integrals and difference-differential equations
Bernoulli numbers are defined by the generating function: et
Certain generalizations of poly-Cauchy numbers of the first and second kind were introduced by Cenkci and Young [7]
Summary
The Cauchy numbers [1,2,3] of the first and second kind, respectively denoted by cn and ĉn , play important roles in many applications in number theory, combinatorics, and in different areas such as approximate integrals and difference-differential equations. Komatsu [2,6] defined poly-Cauchy numbers of the second kind as follows: (k) Certain generalizations of poly-Cauchy numbers of the first and second kind were introduced by Cenkci and Young [7]. These numbers were called Hurwitz-type poly-Cauchy numbers of the first and second kind, (k) denoted by cn ( a) and ĉn ( a), which are respectively defined by:
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
