Note on the Type 2 Degenerate Multi-Poly-Euler Polynomials
Round 1
Reviewer 1 Report
In the paper under review, the authors introduce a novel class of degenerate multi-poly-Euler polynomials and numbers by means of the degenerate multi-polyexponential function and studied their main explicit relations and identities.
The results are new, interesting, and worth to be published. Also, the English writing is acceptable. In conclusion, I recommend this paper for publication in the journal " Symmetry".
Author Response
Dear Editor,
Thank you for your Comments and Suggestions.
Best regards
Reviewer 2 Report
This review paper is valuable and worthwhile for publication because the paper is well written and interested. Recently, i have found closely related to this paper.
Please confirm the following paper and compare the results of this review paper
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Kim, T.; Kim, D.; Kim, H.-Y.; Lee, H.; Jang, L.-C.; Degenerate poly-Bernoulli polynomials arising from degenerate polylogarithm. Adv. Difference Equ. 2020, 444. Kim, T.; Kim, D. S.; Note on the Degenerate Gamma Function. Russ. J. Math. Phys. 27 (2020), no. 3, 352–358. *************************************************Author Response
Dear Reviewer,
Thank you for your Comments and Suggestions.
We have done all revisions. Please see the attached updated version.
Best regards
Author Response File: 
Author Response.pdf
Reviewer 3 Report
Report
on the paper “NOTE ON THE TYPE 2 DEGENERATE MULTI-POLY-EULER POLYNOMIALS” by WASEEM AHMAD KHAN, MEHMET ACIKGOZ, AND UGUR DURAN.
This paper is devoted to the study of the important kind of polynomials - multi-poly-Euler ones. Obtained results can have interesting applications in physics, economics, statistics, probability theory, biology, engineering and other areas.
The authors introduced the type 2 degenerate multi-poly-Euler polynomials and investigated their properties and relations utilizing the degenerate multiple polyexponential functions. In particular, they got the important result showing that type 2 degenerate multi-poly-Euler polynomials are a linear combination of the degenerate Euler polynomials of higher order and the degenerate Stirling numbers of the first kind (Theorem 2).
In addition, an interesting relation between the type 2 degenerate multi-poly-Euler polynomials and degenerate Whitney numbers has been obtained (Theorems 5, 6).
Minor remarks: 1. Shorten the “Introduction and Preliminaries” part.
- Proofreading.
- Correct typos.
By my opinion, the paper “NOTE ON THE TYPE 2 DEGENERATE MULTI-POLY-EULER POLYNOMIALS” by WASEEM AHMAD KHAN, MEHMET ACIKGOZ, AND UGUR DURAN
- is original and doesn’t contradict to ethical or policy issues;
- the question posed by authors is new and well defined;
- the methods used by authors are appropriate;
- the data are sound and well controlled;
- the discussion and conclusions are well balanced;
- the title and abstract convey the obtained results;
- the writing is acceptable;
contains good scientific results and can be published after minor revision.
I declare that I have no competing interests.
Author Response
Dear Reviewer,
Thank you for your Comments and Suggestions.
We have done all revisions. Please see the attached updated version.
Best regards
Author Response File: Author Response.pdf
Reviewer 4 Report
In this article, multi-poly-Euler polynomials are considered throuth the use the degenerate multiple polyexponential functions. As main mathematical contributions, their properties and relations are studied and studied.
The document is well motivated, with nice mathematics, interesting remarks and a clever conclusion. I have only one concern: please adopt the standard “theorem-proof” format. I mean: Theorem: xxx Proof: xxx
In the current version, in some senses, the proof is "before" the theorem statement which may surprise the reader.
If this revision is done, I am in favor of accept this article in Symmetry.
Author Response
Dear Reviewer,
Thank you for your Comments and Suggestions.
We have done all revisions. Please see the attached updated version.
Best regards
Author Response File: Author Response.pdf
