A holonomic systems approach to special functions identities

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We observe that many special functions are solutions of so-called holonomic systems. Bernstein's deep theory of holonomic systems is then invoked to show that any identity involving sums and integrals of products of these special functions can be verified in a finite number of steps. This is partially substantiated by an algorithm that proves terminating hypergeometric series identities, and that is given both in English and in MAPLE.

Original languageEnglish (US)
Pages (from-to)321-368
Number of pages48
JournalJournal of Computational and Applied Mathematics
Issue number3
StatePublished - Dec 10 1990
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics


  • Elimination
  • Weyl algebra
  • computer algebra
  • hypergeometric series
  • partial difference operators

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