Apparent singularities of D-finite systems

Shaoshi Chen, Manuel Kauers, Ziming Li, Yi Zhang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We generalize the notions of ordinary points and singularities from linear ordinary differential equations to D-finite systems. Ordinary points and apparent singularities of a D-finite system are characterized in terms of its formal power series solutions. We also show that apparent singularities can be removed like in the univariate case by adding suitable additional solutions to the system at hand. Several algorithms are presented for removing and detecting apparent singularities. In addition, an algorithm is given for computing formal power series solutions of a D-finite system at apparent singularities.

Original languageEnglish
Pages (from-to)217-237
Number of pages21
JournalJournal of Symbolic Computation
Publication statusPublished - 1 Nov 2019
Externally publishedYes


  • Apparent singularity
  • D-finite system
  • Desingularization
  • Formal power series
  • Gröbner basis
  • Ordinary point


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