On Gould–Hopper-Based Fully Degenerate Poly-Bernoulli Polynomials with a q-Parameter

Round 1

Reviewer 1 Report

In this interesting and well-written paper, the authors consider the fully degenerate Gould-Hopper polynomials with a q parameter and investigate their some properties including difference rule, inversion formula and addition formula. There are also  multifarious correlations and formulas including the fully degenerate Gould-Hopper polynomials with a q parameter, the Gould-Hopper based fully degenerate poly-Bernoulli polynomials with a q parameter and the Gould-Hopper based fully degenerate (α, q)-Stirling numbers of the second kind. For these reasons I think this paper can be published.

Author Response

Dear Professor,

Thanks for your comments.

With my best regards, Ugur

Reviewer 2 Report

This manuscript considered the  fully degenerate Gould-Hopper polynomials with a q parameter and Gould-Hopper based fully degenerate poly-Bernoulli polynomials with a q parameter, and derived some connection formulas which are interesting things.

The proof methods are good, and English is also well-written.

But, authors are corrected the notation of reference.

For example, the reference [13]  " Kim, D., S., Kim, T., Mansour, T., Seo, J.-J." must be corrected by " Kim, D. S., Kim, T., Mansour, T., Seo, J.-J."

If all things are corrected, then I highly recommend this manuscript for publishing your journal.

Author Response

Dear Professor,

Thank you for your comments and suggestions.

I have corrected the notations of the references in my submitted manuscript.

With my best regards, Ugur Duran

Author Response File: Author Response.pdf