Summation in Finite Terms
- 1 April 1981
- journal article
- Published by Association for Computing Machinery (ACM) in Journal of the ACM
- Vol. 28 (2) , 305-350
- https://doi.org/10.1145/322248.322255
Abstract
Results which allow either the computatmn of symbolic solutions to first-order-linear differ- ence equauons or the determination that solutions of a certain form do not exist are presented. Starting with a field of constants, larger fields may be constructed by the formal adjunctlon of symbols whtch behave hke solutions to first-order-linear equations (with a few restrictions) It IS in these extension fields that the difference equations may be posed and m which the solutions are requested. The principal apphcatmn of these results is In finding formulas for a broad class of finite sums or In showing the nonexistence of such formulas.Keywords
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