Open AccessDecision procedure for indefinite hypergeometric summation
Author(s) -
Gosper Rw
Publication year - 1978
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.75.1.40
Subject(s) - mathematics , hypergeometric distribution , property (philosophy) , constant (computer programming) , combinatorics , hypergeometric function , pure mathematics , discrete mathematics , computer science , philosophy , epistemology , programming language
Given a summandan , 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, givenan , finds thoseS (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] and we can also conclude that [Formula: see text] is inexpressible asS (m ) -S (0), for anyS (n ) satisfying Eq. 2.