Solving difference equations in finite terms
Journal of Symbolic Computation
Rational normal forms and minimal decompositions of hypergeometric terms
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Rational canonical forms and efficient representations of hypergeometric terms
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Factoring systems of linear PDEs with finite-dimensional solution spaces
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Differential rational normal forms and a reduction algorithm for hyperexponential func
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Hyperexponential solutions of finite-rank ideals in orthogonal ore rings
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
| Hi-index | 0.00 |
A multivariate hyperexponential function is a function whose"logarithmic derivatives" are rational. Examples ofhyperexponential functions include rational functions, exponentialfunctions, and hypergeometric terms. Hyperexponential functionsplay an important role in the handling of analytic andcombinatorial objects. We present a few algorithms applicable tothe manipulation of hyperexponential functions in an uniformway.Let F be a field of characteristic zero, onwhich derivation operatorsδ1,...,δℓand difference operators (automorphisms)σℓ+1,...,σm act. Let Ebe an F-algebra. Assume that theδi for 1≤ i ≤ ℓ andσj forℓ + 1 ≤ m can be extended toE as derivation and difference operators.Moreover, these operators commute with each other onE. A hyperexponential element ofE over F is defined to be anonzero element h ∈E such thatδ1(h) =r1h,...,δℓ(h)=rℓh,σℓ+1(h)=rℓ+1h,...,σm(h)=rmhfor some r1,...,rm ∈F. These rational functions are called(rational) certificates for h.