Review Reports

Round 1

Reviewer 1 Report

See pdf file

Comments for author File: Comments.pdf

Author Response

Thanks to Reviewer 1 for the recommendation.

The "Abstract" is extended in the revised version.  

Reviewer 2 Report

 

The manuscript is well written, with clarity of ideas, and includes results that may be of the interest of researchers in the area. However, some corrections and clarifications are necessary in order to consider the paper for publication in Mathematics.

1. Page 1, in the right hand side of the first sum, there is an extra $q$ in the denominator.

2. I want to know if the "quintic series" (1) and (2) can be expressed in terms of $q$-polynomials such as: Al-Salam-Carlitz polynomials? Hermite polynomials....?

 

Author Response

Thanks to Reviewer 2 for the comments.

1. The extra ``q" is deleted from the denominator in the right hand side of the first sum in this revised version.
2. The quintic series is (1) and (2) are unlikely expressible in terms of q-analogues of orthogonal polynomials such as Al-Salam-Carlitz and Hermite, since the two sums in (1) and (2) don't have a variable (parameter) except for the summation limit "n".

Reviewer 3 Report

Please see attachement.

Comments for author File: Comments.pdf

Author Response

Thanks to Reviewer 3 for the careful reading and detailed comments.

All the language corrections are applied in this revised version.