A non-holonomic systems approach to special function identities

Authors:
Frédéric Chyzak;Manuel Kauers;Bruno Salvy
Affiliations:
INRIA, Rocquencourt, France;Johannes Kepler University, Linz, Austria;INRIA, Rocquencourt, France
Venue:
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Year:
2009

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Abstract

We extend Zeilberger's approach to special function identities to cases that are not holonomic. The method of creative telescoping is thus applied to definite sums or integrals involving Stirling or Bernoulli numbers, incomplete Gamma function or polylogarithms, which are not covered by the holonomic framework. The basic idea is to take into account the dimension of appropriate ideals in Ore algebras. This unifies several earlier extensions and provides algorithms for summation and integration in classes that had not been accessible to computer algebra before.