• Publications
  • Influence
Rational solutions of linear difference and q-difference equations with polynomial coefficients
  • S. Abramov
  • Mathematics, Computer Science
  • ISSAC '95
  • 1 April 1995
TLDR
A simple algorithm is suggested for the construction of a polynomial divisible by the denominator of any rational solution of the linear difference equation. Expand
  • 110
  • 14
Rational solutions of linear differential and difference equations with polynomial coefficients
Linear differential and difference equations whose coefficients and right-hand sides are polynomials are considered. The problem of constructing all rational solutions of an equation is solved.
  • 130
  • 12
On polynomial solutions of linear operator equations
TLDR
The algorithm described here extends the algorithm to nd all polynomial solutions of di erential and di erence equations that was given in [1, 2] to more general operators. Expand
  • 116
  • 9
On the summation of rational functions
  • 62
  • 9
Rational Normal Forms and Minimal Decompositions of Hypergeometric Terms
TLDR
We describe a multiplicative normal form for rational functions which exhibits the shift structure of the factors, and investigate its properties. Expand
  • 48
  • 8
  • PDF
On solutions of linear functional systems
TLDR
We describe a new direct algorithm for transforming a linear system of recurrences into an equivalent one with nonsingular leading or trailing matrix. Expand
  • 58
  • 7
Minimal decomposition of indefinite hypergeometric sums
TLDR
We present an algorithm which, given a hypergeometric term <i>T</i>(<i>n</i>), constructs hypergeometry terms <i T</i><subscrpt>1</subscRpt>(< i>N</i>) such that the sum of the terms is minimal in some sense. Expand
  • 26
  • 7
  • PDF
Applicability of Zeilberger's algorithm to hypergeometric terms
  • S. Abramov
  • Mathematics, Computer Science
  • ISSAC '02
  • 10 July 2002
TLDR
A terminating condition of the well-known Zeilberger's algorithm for a given hypergeometric term <i>T</i>(<i>n, k</i>) is presented. Expand
  • 32
  • 7
D'Alembertian solutions of linear differential and difference equations
TLDR
D'Alembertian solutions of differential (resp. difference) equations are those expressible as nested indefinite integrals of hyperexponential functions. Expand
  • 71
  • 4
When does Zeilberger's algorithm succeed?
  • S. Abramov
  • Computer Science, Mathematics
  • Adv. Appl. Math.
  • 1 April 2003
TLDR
A terminating condition of the well-known Zeilberger's algorithm for a given hypergeometric term T(n,k) is presented. Expand
  • 48
  • 4
  • PDF