Theory of Summation in Finite Terms

Authors:
Michael Karr
Affiliations:
Software Options Inc., Cambridge, Massachusetts 02138, USA
Venue:
Journal of Symbolic Computation
Year:
1985

Citing 1
Cited 11

Summation in Finite Terms

Journal of the ACM (JACM)

Computer Algebra: Past and Future

Journal of Symbolic Computation
Formal solutions of differential equations

Journal of Symbolic Computation
High degree solutions of low degree equations (extended abstract)

ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Hypergeometric dispersion and the orbit problem

ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Cited References

Computer algebra handbook
Symbolic summation with single-nested sum extensions

ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Summation algorithms for Stirling number identities

Journal of Symbolic Computation
A refined difference field theory for symbolic summation

Journal of Symbolic Computation
Rational solutions of ordinary difference equations

Journal of Symbolic Computation
Polynomial ring automorphisms, rational (w,σ)-canonical forms, and the assignment problem

Journal of Symbolic Computation
Summation in finite terms using sage

ACM Communications in Computer Algebra

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper discusses some of the mathematical aspects of an algorithm for finding formulas for finite sums. The results presented here concern a property of difference fields which show that the algorithm does not divide by zero, and an analogue to Liouville's theorem on elementary integrals.