A holonomic systems approach to special functions identities *

  title={A holonomic systems approach to special functions identities *},
  author={Doron and ZEILBERGER},
  • Published 1990
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. 
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