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Telescoping in the context of symbolic summation in Maple

2004
*
Journal of symbolic computation
*

A design and an implementation

doi:10.1016/j.jsc.2003.08.010
fatcat:lnqitggi7rf5xnash4yaixmwau
*of*a software package which incorporates these methods into*the*computer algebra system*Maple*are described*in*detail. ...*The*focus is on recently-developed results on computing closed forms*of*definite sums*of*hypergeometric terms. ...*The*end result is*the*software package SumTools, a*symbolic**summation*toolbox*in**Maple*.*Symbolic**summation*is a vast research area*in*computer algebra. ...##
###
Index to Volumes 37 and 38

2004
*
Journal of symbolic computation
*

, R.S. and MILLER, J.C.,

doi:10.1016/s0747-7171(04)00109-9
fatcat:q3cckydpknhjhinygacsvlj52y
*Symbolic*computation*of*exact solutions expressible*in*hyperbolic and elliptic functions for nonlinear PDEs, 669 BALLICO, E. and ORECCHIA, F., Computing minimal generators*of**the*... test for (i, j )-uniformity*in*reduced zero-dimensional schemes, 403 AHN, M. ... coefficient bounds, 1507 Special polycyclic generating sequences for finite soluble groups, 1445*Telescoping**in**the**context**of**symbolic**summation**in**Maple*, 1303*The*Cartan matrix and enumerative calculus ...##
###
Creative Telescoping for Holonomic Functions
[chapter]

2013
*
Texts & Monographs in Symbolic Computation
*

*the*impact

*of*creative

*telescoping*

*in*numerous

*contexts*. ... On

*the*other hand, this chapter has

*the*flavour

*of*a survey article:

*the*developments

*in*this area during

*the*last two decades are sketched and a selection

*of*references is compiled

*in*order to highlight ...

*In*

*the*setting

*of*difference fields, Schneider developed a sophisticated

*symbolic*

*summation*theory [86] whose core again is creative

*telescoping*. ...

##
###
A Computer-Algebra-Based Formal Proof of the Irrationality of ζ(3)
[chapter]

2014
*
Lecture Notes in Computer Science
*

We formally prove this result by an a posteriori verification

doi:10.1007/978-3-319-08970-6_11
fatcat:mlorqqxcxbb7dpjx5i53dfmudu
*of*calculations performed by computer algebra algorithms*in*a*Maple*session. ... This result was first proved by Apéry*in*1978, and*the*proof we have formalized follows*the*path*of*his original presentation. ...*The*most notable example being search, that is almost ineffective*in**the**context**of**the*algebraic hierarchy. ...##
###
Greatest Factorial Factorization and Symbolic Summation

1995
*
Journal of symbolic computation
*

We illustrate

doi:10.1006/jsco.1995.1049
fatcat:qha3kq5w6nbkflxuy6qdvwifyu
*the*fundamental role*of*that concept*in**the**context**of**symbolic**summation*. ... Besides a detailed discussion*of**the*basic GFF notions we present a new approach to*the*inde nite rational*summation*problem as well as to Gosper's algorithm for summing hypergeometric sequences. ... One*of*his valuable suggestions for streamlining*the*presentation was to introduce*the*reduction Lemma 3.2. ...##
###
Creative Telescoping on Multiple Sums
[article]

2021
*
arXiv
*
pre-print

*In*particular, we highlight

*the*necessity

*of*

*the*certificate

*in*these computations and how its complexity can greatly influence

*the*computation time. ...

*In*other words, no creative

*telescoping*implementation currently exists that can resolve all these issues automatically. ... We would especially like to acknowledge Pierre Lairez for pointing us to his paper [2] and for demonstrating how to make

*the*computation

*in*Section 3.8 with his binomial sums

*Maple*package. ...

##
###
-XSummer- Transcendental functions and symbolic summation in Form

2006
*
Computer Physics Communications
*

Harmonic sums and their generalizations are extremely useful

doi:10.1016/j.cpc.2005.12.014
fatcat:qswxn37lanazfp7crtaoky7h3u
*in**the*evaluation*of*higher-order perturbative corrections*in*quantum field theory. ...*In*this Letter we discuss*the*implementation*of*several algorithms to solve these sums by algebraic means, using*the*computer algebra system Form. ...*The*work*of*S.M. has been supported*in*part by*the*Helmholtz Gemeinschaft under contract VH-NG-105 and by*the*Deutsche Forschungsgemeinschaft*in*Sonderforschungsbereich/Transregio 9. ...##
###
Creative Telescoping for Parametrised Integration and Summation

2011
*
Les cours du CIRM
*

II-9 Course n o II-Creative

doi:10.5802/ccirm.14
fatcat:5uu7v6zlljda7jlbbqmfxostte
*Telescoping*for Parametrised Integration and*Summation*CHAPTER 2 Early History*of*Creative*Telescoping*Before*the*technical results*in**the*next chapters, I provide a brief ... II-13 Course n o II-Creative*Telescoping*for Parametrised Integration and*Summation*CHAPTER 3 Creative-*Telescoping*Algorithms for Equations*of**the*First Order 1. ...##
###
A series evaluation technique based on a modified Abel lemma

2022
*
Turkish Journal of Mathematics
*

We introduce a technique for determining infinite series identities through something

doi:10.55730/1300-0098.3177
fatcat:xmfb6uv4fveqjkxnvwqjyzqgj4
*of*a combination*of**the*modified Abel lemma on*summation*by parts and a method*of*undetermined coefficients. ... We succeed*in*applying our technique*in*our proving a nontrivial variant*of*Gauss' hypergeometric identity, giving us an evaluation for a family*of*3F2(1) -series with three free parameters, and to establish ...*The*second author is*the*member*of**the*Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA)*of**the*Istituto Nazionale di Alta Matematica (INdAM). ...##
###
Definite Sums of Hypergeometric Terms and Limits of P-Recursive Sequences
[article]

2017
*
arXiv
*
pre-print

*The*ubiquity

*of*

*the*class

*of*D-finite functions and P-recursive sequences

*in*

*symbolic*computation is widely recognized.

*In*this thesis,

*the*presented work consists

*of*two parts related to this class. ...

*In*

*the*first part, we generalize

*the*reduction-based creative

*telescoping*algorithms to

*the*hypergeometric setting, which allows to deal with definite sums

*of*hypergeometric terms more quickly. ...

*In*

*the*study

*of*

*symbolic*

*summation*, there are mainly two kinds

*of*problems related to hypergeometric terms. Problem 1.1 (Hypergeometric

*summation*). ...

##
###
Ten Problems in Experimental Mathematics

2006
*
The American mathematical monthly
*

It should be mentioned that both

doi:10.1080/00029890.2006.11920330
fatcat:7biryus4jvckjbraro3d3h2afm
*Maple*and*the*ISC identified*the*constant ζ(3, 1) (see*the*remark under*the*"history and*context*" heading). ...*In*such cases,*the*Euler-Maclaurin*summation*formula [2, p. 180] can be invoked to conclude that*the*error E(h)*in**the*approximation (28) decreases very rapidly-faster than any power*of*h. ... which reduces*the*given double Euler sums to a sum*of*products*of*classical ζ-values. Euler also noted*the*first reflection formulas certainly valid when a > 1 and b > 1. ...##
###
Ten Problems in Experimental Mathematics

2006
*
The American mathematical monthly
*

It should be mentioned that both

doi:10.2307/27641975
fatcat:p5deks7g7jepfh4u2g2tmzyh64
*Maple*and*the*ISC identified*the*constant ζ(3, 1) (see*the*remark under*the*"history and*context*" heading). ...*In*such cases,*the*Euler-Maclaurin*summation*formula [2, p. 180] can be invoked to conclude that*the*error E(h)*in**the*approximation (28) decreases very rapidly-faster than any power*of*h. ... which reduces*the*given double Euler sums to a sum*of*products*of*classical ζ-values. Euler also noted*the*first reflection formulas certainly valid when a > 1 and b > 1. ...##
###
Deconstructing the Zeilberger algorithm†

2005
*
Journal of difference equations and applications (Print)
*

Hence WZ theory is transgressing

doi:10.1080/10236190500089911
fatcat:ckqbmjeexbdg3ereoge7xy65de
*the*boundaries*of**the**context**of*justification into*the**context**of*discovery. ...*The*accompanying*Maple*package FindHypergeometric explains*the*various miracles that account for*the*classical evaluations, and*the*more specialized*Maple*package twoFone, also accompanying this article ...*In*particular,*the*Zeilberger algorithm (as implemented*in*my own*Maple*package EKHAD, and starting with*Maple*6,*in**the*built-*in*package SumTools[Hypergeometric], and there is a very popular Mathematica ...##
###
Automatic Improvements of Wallis' Inequality

2010
*
2010 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
*

*In*

*the*main part

*of*

*the*article we automatically refine

*the*bounds

*in*Wallis' inequality by using methods based on Collins' cylindrical algebraic decomposition. ...

*The*mathematical backbone

*of*this article is formed by three classical formulas

*of*Wallis: his product formula for π, an inequality implying

*the*product formula

*in*

*the*limit, and a related definite integral ... Evaluation by creative

*telescoping*

*The*definite integration problem can be transformed into a definite

*summation*problem. ...

##
###
Efficient Algorithms for Mixed Creative Telscoping

2016
*
Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '16
*

Its analysis reveals tight bounds on

doi:10.1145/2930889.2930907
dblp:conf/issac/BostanDS16
fatcat:kzmyji4yz5f5pfnvqtxfhllv7q
*the*sizes*of**the**telescoper*it produces. ... Creative*telescoping*is a powerful computer algebra paradigm -initiated by Doron Zeilberger*in**the*90's- for dealing with definite integrals and sums with parameters. ... We are grateful to*the*referees for their thorough work and helpful comments. This work has been supported*in*part by FastRelax ANR-14-CE25-0018-01. ...
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