REDUCE package for the indefinite and definite summation
نویسندگان
چکیده
منابع مشابه
Algorithms for the Indefinite and Definite Summation
The celebrated Zeilberger algorithm which finds holonomic recurrence equations for definite sums of hypergeometric terms F (n, k) is extended to certain nonhypergeometric terms. An expression F (n, k) is called hypergeometric term if both F (n + 1, k)/F (n, k) and F (n, k+1)/F (n, k) are rational functions. Typical examples are ratios of products of exponentials, factorials, Γ function terms, b...
متن کاملOn rational definite summation
We present a partial proof of van Hoeij-Abramov conjecture about the algorithmic possibility of computation of finite sums of rational functions. The theoretical results proved in this paper provide an algorithm for computation of a large class of sums (1).
متن کاملIndefinite Summation and the Kronecker Delta
Indefinite summation, together with a generalized version of the Kronecker delta, provide a calculus for reasoning about various polynomial functions that arise in combinatorics, such as the Tutte, chromatic, flow, and reliability polynomials. In this paper we develop the algebraic properties of the indefinite summation operator and the generalized Kronecker delta from an axiomatic viewpoint. O...
متن کاملDecision procedure for indefinite hypergeometric summation.
Given a summand a(n), we seek the "indefinite sum" S(n) determined (within an additive constant) by [Formula: see text] or, equivalently, by [Formula: see text] An algorithm is exhibited which, given a(n), finds those S(n) with the property [Formula: see text] With this algorithm, we can determine, for example, the three identities [Formula: see text] [Formula: see text] and [Formula: see text]...
متن کاملIndefinite summation with unspecified summands
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.
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ژورنال
عنوان ژورنال: ACM SIGSAM Bulletin
سال: 1995
ISSN: 0163-5824
DOI: 10.1145/216685.216687