On computing the coefficients of bivariate holonomic formal series

Authors:
P. Massazza;R. Radicioni
Affiliations:
Università degli Studi dell'Insubria, Dipartimento di Informatica e Comunicazione, Varese, Italy;Università degli Studi di Milano, Dipartimento di Scienze dell'Informazione, Milano, Italy
Venue:
Theoretical Computer Science - In memoriam: Alberto Del Lungo (1965-2003)
Year:
2005

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Abstract

In this work, we study the problem of computing the coefficients of holonomic formal series in two commuting variables. Given a formal series φ(x, y) = Σn,k ≥ 0 cnkxnyk specified by a holonomic system Σj=0d1 pj(x, y)∂xjφ = 0 and Σj=0d2qj(x, y)∂yjφ = 0 with a suitable finite set of intial conditions {[xayb]φ(x, y)}, we show that the coefficient [xiyj]φ(x, y) can be computed in time O(i + j) under the uniform cost criterion.