Two-Variable Type 2 Poly-Fubini Polynomials

Round 1

Reviewer 1 Report

The authors are concerned with a new extension of the two-variable Fubini polynomials. It is introduced by means of the polyexponential function. The new polynomials are called the two-variable type 2 poly-Fubini polynomials. Some useful relations, including the Stirling numbers of the second and the first kinds, the usual Fubini polynomials, and the higher-order Bernoulli polynomials are also derived.

The manuscript is written using a fairly basic mathematics (algebra). The results seem correct but we have to report a series of ambiguities.

A lot of proven results need to be formalized as lemmas or properties, see the relationships (18), (19), the relationship contained in lines  56-57, again the relationships (22), (27), (28), 29), (31), (32), (35), (36), (37), (40) and (41), (42) and the last result (43). It has to be formulated as a Theorem.

In the proof of (18) a summation sign Σ seems to be missing (see lines 44-45).

After checking and very carefully correcting the entire manuscript, we consider it to be publishable.

 

Author Response

Dear Editor,

Thank you so much for you all comments and corrrections, which improved my-coauthored paper.

Some of your corrections are due to converting original tex style to Mathematics tex style. 

The other corrections have revisited one by one.

With my best regards

 

Reviewer 2 Report

See the attached file.

Comments for author File: Comments.pdf

Author Response

Dear Editor,

Thank you so much for you all comments and corrrections, which improved my-coauthored paper.

Some of technical corrections are due to converting original tex style to Mathematics tex style. 

The other corrections have revisited one by one.

With my best regards