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Peer-Review Record

On Summation of Fourier Series in Finite Form Using Generalized Functions

Mathematics 2025, 13(3), 538; https://doi.org/10.3390/math13030538
by Ksaverii Malyshev 1,2,*, Mikhail Malykh 1,3,*, Leonid Sevastianov 1,3 and Alexander Zorin 1
Reviewer 1:
Reviewer 2:
Reviewer 3: Anonymous
Mathematics 2025, 13(3), 538; https://doi.org/10.3390/math13030538
Submission received: 29 December 2024 / Revised: 4 February 2025 / Accepted: 5 February 2025 / Published: 6 February 2025
(This article belongs to the Section E4: Mathematical Physics)

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

See in the attachment

Comments for author File: Comments.pdf

Author Response

Hello, dear Referee! Our response to the comments is attached.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Please see the attachment.

Comments for author File: Comments.pdf

Author Response

Hello, dear Referee! Our response to the comments is attached.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript considers the problem of obtaining a final expression for a function initially given in the form of a trigonometric Fourier series whose coefficients are rational functions of the summation index. The work is written in good language, mathematically correct. All the main statements made are proved. The authors obtained significant results that deserve publication. I have a few minor comments.

1. It would be nice to describe the calculation of $\hat C$ in more detail.

2. It would be nice to clarify how another well-known equality

$\sum_{n=1}^\infty\frac{sin nx}{n}=\frac{\pi-x}2$ relates to (3).

3. Typo. Probably under Figure 1 there should be a reference to Example 2.

4. There are no red lines in Figure 2. Either remove the mention of the red lines or make them visible.

Author Response

Hello, dear Referee! Our response to the comments is attached.

Author Response File: Author Response.pdf

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