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On the link between binomial theorem and discrete convolution

Home Page: https://kolosovpetro.github.io/pdf/OnTheBinomialTheoremAndDiscreteConvolution.pdf

License: MIT License

TeX 100.00%

binomial-theorem polynomials math mathematics open-research open-science research research-project

onthebinomialtheoremanddiscreteconvolution's Introduction

On the link between binomial theorem and discrete convolution

What is all about

Source code of the manuscript entitled "On the link between binomial theorem and discrete convolution" along with Mathematica programs in order to verify results.

Build and run in Intellij IDEA

Install MikTeX: https://miktex.org/download
Update MikTeX
Install SumatraPDF viewer: https://www.sumatrapdfreader.org/download-free-pdf-viewer
Install Intellij IDEA Ultimate: https://www.jetbrains.com/idea/download/#section=windows
Activate Intellij IDEA Ultimate
Install TeXiFy IDEA plugin: https://plugins.jetbrains.com/plugin/9473-texify-idea
Clone this repository locally: https://github.com/kolosovpetro/OnTheBinomialTheoremAndDiscreteConvolution.git
Open github-latex-template folder in Intellij IDEA Ultimate and configure as follows
- LaTeX Configuration
- BibTeX Configuration
Configure Inverse Search in Intellij IDEA for SumatraPDF: Tools -> LaTeX -> Configure Inverse Search
Compile document using Shift + F10

How to use Mathematica package

Open the package file OnTheBinomialTheoremAndDiscreteConvolution.m in Wolfram Mathematica, I use version 13.0
Execute the package using Shift+Enter
Open the notebook file OnTheBinomialTheoremAndDiscreteConvolution.nb
Execute the line: Needs["OnTheBinomialTheoremAndDiscreteConvolution"]
Continue your work as desired

Configure CI / CD

Set repository secrets

GH_ACCESS_TOKEN: Generate Github Personal access token at Settings -> Developer Settings -> Personal access tokens -> Generate mew token and assign in to secret GH_ACCESS_TOKEN
GH_NAME: Your Github username
GH_EMAIL: Your Github email

Actions and their trigger policy

build-pdf.yml builds project using TeXLive. Triggered on pull_request, push to develop branch
build-and-deploy-pdf.yml builds project using TeXLive and deploys to GitHub Pages. Triggered on push to main branch

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onthebinomialtheoremanddiscreteconvolution's Issues

ARXIV-1603-2. Add a mathematica program that returns \left[ \sum_{j=0}^{r} \frac{1}{(-1)^j} \binom{r}{j} \sum_{k=0}^{b-1} k^{2r-j} \right], see page 5 of the manuscript

ARXIV-1603-2. Add a mathematica program that returns \left[ \sum_{j=0}^{r} \frac{1}{(-1)^j} \binom{r}{j} \sum_{k=0}^{b-1} k^{2r-j} \right], see page 5 of the manuscript.

TODO:

Create a mathematica program such that evaluates an identity \sum_{r=0}^{m} (-1)^{r} x^{r} \coeffA{m}{r} \polynomialT{r}{b-1}
In section "Verification of the results" add an example of recall of such method

ARXIV-1603-5. Add annex with the long list of polynomials P.

TODO:

Create mathematica program which lists the polynomials P for particular m and prints N rows.
Add annex to the TeX document with these polynomials
Add txt file with these polynomials to the repository, create speficied folder if necessary

ARXIV-1603-1. Add a mathematica script to repoduce table 1 that is table of coefficients A(m,r).

ARXIV-1603-1. Add a mathematica script to repoduce table 1 that is table of coefficients A(m,r).

ARXIV-1603-7. Add annex with long list of polynomials L.

TODO:

Create mathematica program which lists the polynomials P for particular m and prints N rows.
Add annex to the TeX document with these polynomials
Add txt file with these polynomials to the repository, create speficied folder if necessary

ARXIV-1603-3. Update documentation of the mathematica package OnTheBinomialTheoremAndDiscreteConvolution.m. Documentation should describe the entire use and also contain a few examples of use.

ARXIV-1603-3. Update documentation of the mathematica package OnTheBinomialTheoremAndDiscreteConvolution.m. Documentation should describe the entire use and also contain a few examples of use.

ARXIV-1603-6. Add annex with the long list of generalized polynomials P.

TODO:

Create mathematica program which lists the generalized polynomials P for particular m and prints N rows.
Add annex to the TeX document with these polynomials
Add txt file with these polynomials to the repository, create speficied folder if necessary

ARXIV-1603-4. Create a documentation of the package OnTheBinomialTheoremAndDiscreteConvolution.m in TeX format. Place it to the same repository, but compile separately.

ARXIV-1603-4. Create a documentation of the package OnTheBinomialTheoremAndDiscreteConvolution.m in TeX format. Place it to the same repository, but compile separately.

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