Matches in SemOpenAlex for { <https://semopenalex.org/work/W2474345694> ?p ?o ?g. }
Showing items 1 to 81 of
81
with 100 items per page.
- W2474345694 endingPage "150" @default.
- W2474345694 startingPage "150" @default.
- W2474345694 abstract "Zeilberger's algorithm has been shown to be a very useful tool in a wide range of applications. These include finding closed forms of definite sums of hypergeometric terms, certifying large classes of identities in combinatorics and in the theory of special functions, and asymptotic estimates. Regardless of the extensive work on the algorithm, there still exist many interesting problems arising out of the algorithm, and a number of them were not considered or solved by the “classics”. In this thesis we address two key problems: (a) the limitations in the domain of applicability of Zeilberger's algorithm and (b) the efficiency of the algorithm. We present new algorithms which help solve or alleviate these problems. For applicability, we establish a criterion for the termination of the algorithm for the rational function case, and describe an algorithm which uses this criterion to determine the applicability of Zeilberger's algorithm. We also summarize Abramov's result on applicability for the general hypergeometric case. For efficiency, we present an algorithm which computes the minimal telescopers directly and efficiently for the rational function case, and an algorithm which computes a non-trivial lower bound for the order of the telescopers for the general hypergeometric case. We describe a Maple implementation of the package Telescopers for computing the minimal Z-pairs. The package is a sub-package of the package Hypergeometric, a Maple toolbox for working with hypergeometric terms in general, and for computing closed forms of indefinite and definite sums of hypergeometric terms in particular. In the context of symbolic summation, the package Hypergeometric becomes a sub-package of the package SumTools, a Maple summation toolbox." @default.
- W2474345694 created "2016-07-22" @default.
- W2474345694 creator A5002316838 @default.
- W2474345694 creator A5009665287 @default.
- W2474345694 creator A5066677758 @default.
- W2474345694 date "2003-01-01" @default.
- W2474345694 modified "2023-09-22" @default.
- W2474345694 title "Algorithms for the construction of the minimal telescopers" @default.
- W2474345694 hasPublicationYear "2003" @default.
- W2474345694 type Work @default.
- W2474345694 sameAs 2474345694 @default.
- W2474345694 citedByCount "3" @default.
- W2474345694 crossrefType "journal-article" @default.
- W2474345694 hasAuthorship W2474345694A5002316838 @default.
- W2474345694 hasAuthorship W2474345694A5009665287 @default.
- W2474345694 hasAuthorship W2474345694A5066677758 @default.
- W2474345694 hasConcept C11413529 @default.
- W2474345694 hasConcept C136119220 @default.
- W2474345694 hasConcept C14036430 @default.
- W2474345694 hasConcept C151730666 @default.
- W2474345694 hasConcept C158241908 @default.
- W2474345694 hasConcept C165175332 @default.
- W2474345694 hasConcept C176671685 @default.
- W2474345694 hasConcept C197320386 @default.
- W2474345694 hasConcept C199360897 @default.
- W2474345694 hasConcept C202444582 @default.
- W2474345694 hasConcept C2777655017 @default.
- W2474345694 hasConcept C2779343474 @default.
- W2474345694 hasConcept C33923547 @default.
- W2474345694 hasConcept C41008148 @default.
- W2474345694 hasConcept C60400383 @default.
- W2474345694 hasConcept C75190567 @default.
- W2474345694 hasConcept C78458016 @default.
- W2474345694 hasConcept C86803240 @default.
- W2474345694 hasConceptScore W2474345694C11413529 @default.
- W2474345694 hasConceptScore W2474345694C136119220 @default.
- W2474345694 hasConceptScore W2474345694C14036430 @default.
- W2474345694 hasConceptScore W2474345694C151730666 @default.
- W2474345694 hasConceptScore W2474345694C158241908 @default.
- W2474345694 hasConceptScore W2474345694C165175332 @default.
- W2474345694 hasConceptScore W2474345694C176671685 @default.
- W2474345694 hasConceptScore W2474345694C197320386 @default.
- W2474345694 hasConceptScore W2474345694C199360897 @default.
- W2474345694 hasConceptScore W2474345694C202444582 @default.
- W2474345694 hasConceptScore W2474345694C2777655017 @default.
- W2474345694 hasConceptScore W2474345694C2779343474 @default.
- W2474345694 hasConceptScore W2474345694C33923547 @default.
- W2474345694 hasConceptScore W2474345694C41008148 @default.
- W2474345694 hasConceptScore W2474345694C60400383 @default.
- W2474345694 hasConceptScore W2474345694C75190567 @default.
- W2474345694 hasConceptScore W2474345694C78458016 @default.
- W2474345694 hasConceptScore W2474345694C86803240 @default.
- W2474345694 hasLocation W24743456941 @default.
- W2474345694 hasOpenAccess W2474345694 @default.
- W2474345694 hasPrimaryLocation W24743456941 @default.
- W2474345694 hasRelatedWork W1480383020 @default.
- W2474345694 hasRelatedWork W1484592850 @default.
- W2474345694 hasRelatedWork W1532229204 @default.
- W2474345694 hasRelatedWork W1980891595 @default.
- W2474345694 hasRelatedWork W1995176999 @default.
- W2474345694 hasRelatedWork W2000852057 @default.
- W2474345694 hasRelatedWork W2022837326 @default.
- W2474345694 hasRelatedWork W2051580005 @default.
- W2474345694 hasRelatedWork W2119126401 @default.
- W2474345694 hasRelatedWork W21277445 @default.
- W2474345694 hasRelatedWork W2130918732 @default.
- W2474345694 hasRelatedWork W2153663440 @default.
- W2474345694 hasRelatedWork W2395656192 @default.
- W2474345694 hasRelatedWork W2550175546 @default.
- W2474345694 hasRelatedWork W2779329448 @default.
- W2474345694 hasRelatedWork W2798316719 @default.
- W2474345694 hasRelatedWork W2961504112 @default.
- W2474345694 hasRelatedWork W3042757152 @default.
- W2474345694 hasRelatedWork W3101467985 @default.
- W2474345694 hasRelatedWork W3102099803 @default.
- W2474345694 isParatext "false" @default.
- W2474345694 isRetracted "false" @default.
- W2474345694 magId "2474345694" @default.
- W2474345694 workType "article" @default.