Generalized Summation Formulas for the Kampé de Fériet Function

Round 1

Reviewer 1 Report

In my point of view this is a well-exposed, well-planned and well-reviewed work. It also seems to me to be a well done job, in the sence that it does exactly what it says it is intended to do. 

I don't have any questions other than the following:

1. Line 46, with the sentence '...formulas were related to the cases H + A = 3 and G + C = 2', it is not clear to me whether the authors refer the case where both the conditions 'H+A=3' and 'G+C=2' are to be considered together, as a conjunction, or whether a cases where 'H+A=3' and a cases where 'G+C=2' are considered. Please consider to rephrase this sentence.
2. In the proof for Theorem 4, the authors refer to formulas (10) and (11) and I think they are using formulas (12) and (13).
3. To complete the same proof, I think we need the formula \Gamma(-(i+1))/\Gamma(-1)=(-1)^i/(i+1)!. If so, the use of this formula must be explicit and justified, or an alternative way must be presented.
4. There are two errors in the title of reference 25. Where it is "of ordre" must be "d'ordre" and "aˇ deux" must be "à deux".

Author Response

Dear Reviewers,

Our answer is given in the attached pdf file "cover-letter-Revised-Version(19.11.21).pdf".

Best regards,   Gradimir Milovanovic

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper is well-written, and the results are new and interesting for those that work in this field of interest.

The strong points of the article are:

1. The methods used in the proofs are correct, clear and concise;
2. The article is clearly and correctly written;
3. The paper could be easily read by a specialist in this field;
4. Each theorem is followed by remarks that show how the theorem generalize some previous results obtained by different authors;
5. The "References" are well choose, and cover the main subject of this article.

Since I didn't saw any weak points, I recommend to publish the paper as it is now.

Author Response

Dear Reviewers,

Our answer is given in the attached pdf file "cover-letter-Revised-Version(19.11.21).pdf".

Best regards,   Gradimir Milovanovic

Author Response File: Author Response.pdf