Dr. Bertrand Teguia Tabuguia, Ph.D.

A mathematics lover!

Collaborative papers

• Concatenations of Terms of an Arithmetic Progression.
  With Luca, Florian. A substantial revision of
  Explicit formulas for concatenations of arithmetic progressions.
  May 2024. Submitted.
  
• On Rational Recursion for Holonomic Sequences.
  With Worrell, James. To appear in the Proceedings of CASC'24.
  April 2024. Supplementary files.
  
• D-Algebraic Functions.
  With Ait El Manssour, Rida and Sattelberger, Anna-Laura.
  Illustrations, software, and examples. Submitted. January 2023.
• On the Representation of Non-Holonomic Univariate Power Series.
  Teguia Tabuguia, Bertrand and Koepf, Wolfram.
  Maple Trans. 2, 1. Article 14315, 18 pages.
  August 2022.
• FPS in action: an easy way to find explicit
  formulas for interlaced hypergeometric sequences.
  Teguia Tabuguia, Bertrand and Koepf, Wolfram.
  ACM Communication in Computer Algebra. Volume 56, Issue 2. June 2022, pp 46-50. Pdf.
  Poster presentation at ISSAC'22.
• Symbolic Conversion of Holonomic Functions to Hypergeometric-Type Power Series.
  Teguia Tabuguia, Bertrand and Koepf, Wolfram.
  Computer Algebra issue of the Journal of Programming and Computer Software. April 2022. Volume 48. Pages 125-146. Preprint version.
• Hypergeometric-Type Power Series.
  Teguia Tabuguia, Bertrand and Koepf, Wolfram.
  Extended Abstract for the 4th International Conference "Computer Algebra", Moscow.
  Pages 105-108. June 2021.
• Power Series Representations of Hypergeometric-Type Functions.
  Teguia Tabuguia, Bertrand and Koepf, Wolfram.
  In Corless R., Gerhard J., Kotsireas I. (eds): Maple in Mathematics Education and Research. MC 2020. Communications in Computer and Information Science, Springer.

Personal Papers

• Computing with Hypergeometric-Type Terms.
  Teguia Tabuguia, Bertrand.
  April 2024. Accepted as Software Demonstration for ISSAC'24.
• Hypergeometric-Type Sequences.
  Teguia Tabuguia, Bertrand.
  Journal of Symbolic Computation.
  DOI: https://doi.org/10.1016/j.jsc.2024.102328. 
  Software and examples (GitHub).
  
• Arithmetic of D-Algebraic Functions.
  Teguia Tabuguia, Bertrand. Journal of Symbolic Computation
  MathRepo page.  May 2023 - June 2024 (publication).
  DOI: https://doi.org/10.1016/j.jsc.2024.102348
• Operations for D-algebraic Functions.
  Teguia Tabuguia, Bertrand.
  ACM Communications in Computer Algebra, Volume 57, Issue 2. Pages 51--56. June 2023.
  Visit this MathRepo repository.
  
• Guessing with Quadratic Differential Equations.
  Teguia Tabuguia, Bertrand.
  Software presentation at ISSAC'22. ACM Communications in Computer Algebra.
  July 2022. Pdf. Illustration.
•  A variant of van Hoeij's algorithm to compute hypergeometric
  term solutions of holonomic recurrence equations.
  Teguia Tabuguia, Bertrand.
  J. Algorithm Comput. Volume 53, Issue 2. pp 1-32. December 30, 2021.
  Maxima code. Comparison.
• An Algorithmic Random-Integer Generator based
  on the Distribution of Prime Numbers.
  Teguia Tabuguia, Bertrand.
  Research Journal of Mathematics and Computer Science, 2019; 3:16. DOI: 10.28933/rjmcs-2019-06-1705.
• On 'Best' Rational Approximations to $\pi$ and $\pi+e$.
  Teguia Tabuguia, Bertrand.
  Preprints 2020, 2020050268. DOI: 10.20944/preprints202005.0268.v2. Maxima code. (General mathematics manipulations. Draft of an idea!). Soon to be improved (2024).
  

The differential equation in ADE encodes the Weierstrass elliptic functions. The command invDalg from the package NLDE computes a differential equation for the functional inverses of Weirstrass elliptic functions.

The first command solves the recurrence equation with the initial values in the list, and the second command simplifies the given trigonometric expression. The terms denoted with the Greek symbols represent the interlacements (or interleavings) involved in these sequences. The commands are from my package HyperTypeSeq.