Elsevier

Discrete Mathematics

Volume 306, Issue 17, 6 September 2006, Pages 2073-2083
Discrete Mathematics

Indefinite summation with unspecified summands

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Abstract

We provide a new algorithm for indefinite nested summation which is applicable to summands involving unspecified sequences x(n). More than that, we show how to extend Karr's algorithm to a general summation framework by which additional types of summand expressions can be handled. Our treatment of unspecified sequences can be seen as a first illustrative application of this approach.

Keywords

Combinatorial identities
Symbolic summation
Difference fields

Cited by (0)

1

Partially supported by the Austrian Science Foundation (FWF) Grant F1305 and the German Academic Exchange Service (DAAD) Grant D/03/40515.

2

Supported by the SFB-Grant F1305 and by Grant P16613-N12 of the Austrian FWF.