Multibasic and mixed hypergeometric Gosper-type algorithms
From MaRDI portal
Publication:1974697
DOI10.1006/jsco.1999.0321zbMath0973.33010OpenAlexW1970359497WikidataQ115902554 ScholiaQ115902554MaRDI QIDQ1974697
Publication date: 8 May 2000
Published in: Journal of Symbolic Computation (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/6e7d6a4e242c43242668de1bd3e1393f3ac87925
Gosper algorithmgreatest factorial factorizationhypergeometric solutions of equationspolynomial solutions of recurrence equations
Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10) Bibasic functions and multiple bases (33D65)
Related Items
Telescoping in the context of symbolic summation in Maple, Solving parameterized linear difference equations in terms of indefinite nested sums and products, Constructing minimal telescopers for rational functions in three discrete variables, Refined telescoping algorithms in RΠΣ -extensions to reduce the degrees of the denominators✱, Representation of hypergeometric products of higher nesting depths in difference rings, Proof of a conjecture of Lundow and Rosengren on the bimodality of \(p,q\)-binomial coefficients, Summation theory. II: Characterizations of \(R {\Pi}{\Sigma}^{\ast}\)-extensions and algorithmic aspects, Minimal representations and algebraic relations for single nested products, A refined difference field theory for symbolic summation, Parameterized telescoping proves algebraic independence of sums, Algorithms for \(q\)-hypergeometric summation in computer algebra, A difference ring theory for symbolic summation, Polynomial ring automorphisms, rational \((w,\sigma )\)-canonical forms, and the assignment problem, Structural theorems for symbolic summation, SIMPLIFYING SUMS IN ΠΣ*-EXTENSIONS, On rational and hypergeometric solutions of linear ordinary difference equations in \(\Pi\Sigma^\ast\)-field extensions, Telescoping method, summation formulas, and inversion pairs, Simplifying Multiple Sums in Difference Fields, Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation, Representation of hypergeometric products in difference rings
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The method of differentiating under the integral sign
- An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities
- A fast algorithm for proving terminating hypergeometric identities
- The method of creative telescoping
- Hypergeometric solutions of linear recurrences with polynomial coefficients
- Rational solutions of linear difference and \(q\)-differential equations with polynomial coefficients
- On Zeilberger's algorithm and its \(q\)-analogue
- An introduction to pseudo-linear algebra
- A generalization of Gosper's algorithm to bibasic hypergeometric summation
- \(q\)-hypergeometric solutions of \(q\)-difference equations
- Greatest factorial factorization and symbolic summation
- Decision procedure for indefinite hypergeometric summation