SIGMA swMATH ID: 6904 Software Authors: Carsten Schneider Description: Sigma is a Mathematica package that can handle multisums in terms of indefinite nested sums and products. The summation principles of Sigma are: telescoping, creative telescoping and recurrence solving. The underlying machinery of Sigma is based on difference field theory. The package has been developed by Carsten Schneider, a member of the RISC Combinatorics group. Homepage: http://www.risc.jku.at/research/combinat/software/Sigma/index.php/ Dependencies: Mathematica Keywords: multisums; difference field theory; telescoping; recurrence solving Related Software: qZeil; Mathematica; EvaluateMultiSums; gfun; OEIS; GeneratingFunctions; MultiZeilberger; qMultiSum; HarmonicSums; HolonomicFunctions; MultiSum; DLMF; Dependencies; RatDiff; Telescopers; RhoSum; qZEILBERGER; ZEILBERGER; NewZeil.m; SumCracker Cited in: 106 Publications Further Publications: http://www.risc.jku.at/people/cschneid/Sigma/Sigma.html Standard Articles 3 Publications describing the Software, including 3 Publications in zbMATH Year Symbolic summation assists combinatorics. Zbl 1188.05001Schneider, Carsten 2006 A new Sigma approach to multi-summation. Zbl 1078.33021Schneider, Carsten 2005 The summation package Sigma: underlying principles and a rhombus tiling application. Zbl 1066.68164Schneider, Carsten 2004 all top 5 Cited by 94 Authors 30 Schneider, Carsten 12 Liu, Jicai 6 Blümlein, Johannes 6 Kauers, Manuel 6 Prodinger, Helmut 5 Mao, Guo-Shuai 5 Wei, Chuanan 4 Paule, Peter 4 Uncu, Ali Kemal 3 Chu, Wenchang 3 Hou, Qinghu 3 Pillwein, Veronika 3 Wang, Chen 2 Ablinger, Jakob 2 Amdeberhan, Tewodros 2 Chen, William Yong-Chuan 2 Chen, Xiaojing 2 Driver, Kathy A. 2 Garoufalidis, Stavros 2 Guo, Victor J. W. 2 Klein, Sebastian 2 Koutschan, Christoph 2 Krattenthaler, Christian Friedrich 2 Moll, Victor Hugo 2 Mu, Yanping 2 Osburn, Robert 2 Stan, Flavia 2 Sun, Xinyu 2 Wang, Jun 2 Wang, Ronghua 2 Weideman, J. André C. 2 Wong, Elaine 2 Zudilin, Wadim 1 Abramov, Sergeĭ Aleksandrovich 1 Andrews, George Eyre 1 Aumüller, Martin 1 Batir, Necdet 1 Bećirović, A. 1 Berkovich, Alexander 1 Beuchler, Sven 1 Bian, Ke-Xin 1 Brent, Richard Peirce 1 Bronstein, Manuel Eric 1 Buchta, Christian 1 Chen, Jiayu 1 Chen, Kwang-Wu 1 Chen, Shaoshi 1 Chestnov, Vsevolod 1 Choi, Byoung Kyu 1 Corcino, Roberto Bagsarsa 1 Dietzfelbinger, Martin 1 Dixit, Atul 1 Gerhold, Stefan 1 Glebsky, Lev Yu. 1 Guan, Xiao 1 Heuberger, Clemens 1 Jana, Arijit 1 Jin, Hai-Tao 1 Jiu, Lin 1 Kalita, Gautam 1 Kang, DongHun 1 Kim, Seon-Hong 1 Krenn, Daniel 1 Kuba, Markus F. 1 Liu, Hongmei 1 Marquard, Peter 1 Moch, Sven-Olaf 1 Papathanasiou, Georgios 1 Petkovšek, Marko 1 Riese, Axel 1 Round, Mark 1 Rowland, Eric S. 1 Schmidt, Maxie Dion 1 Schöberl, Joachim 1 Schönwald, Kay 1 Straub, Armin 1 Sulzgruber, Robin 1 Van Thurenhout, S. 1 Velizhanin, V. N. 1 Vignat, Christophe 1 Wagner, Stephan G. 1 Wang, Jie 1 Wang, Qin 1 Wang, Weiping 1 Wang, Xiaoxia 1 Warnaar, S. Ole 1 Weiss, Howard 1 Wiart, Jaspar 1 Yao, Yukun 1 Yu, Yuanbo 1 Zaglmayr, Sabine 1 Zhang, Huajun 1 Zima, Eugene V. 1 Zimmermann, Burkhard all top 5 Cited in 43 Serials 11 Journal of Symbolic Computation 7 Journal of Difference Equations and Applications 6 Journal of Mathematical Analysis and Applications 6 Advances in Applied Mathematics 5 Results in Mathematics 4 The Electronic Journal of Combinatorics 4 The Ramanujan Journal 4 Integers 3 Discrete Mathematics 3 Proceedings of the American Mathematical Society 3 Mathematics in Computer Science 2 Computer Physics Communications 2 Nuclear Physics. B 2 Journal of Combinatorial Theory. Series A 2 Applicable Algebra in Engineering, Communication and Computing 2 Integral Transforms and Special Functions 2 Journal of High Energy Physics 2 International Journal of Number Theory 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Advances in Applied Probability 1 Bulletin of the Australian Mathematical Society 1 Indian Journal of Pure & Applied Mathematics 1 Mathematics of Computation 1 Annales de l’Institut Fourier 1 Colloquium Mathematicum 1 Computing 1 The Fibonacci Quarterly 1 Journal of Computational and Applied Mathematics 1 Mathematics and Computers in Simulation 1 Programming and Computer Software 1 European Journal of Combinatorics 1 Chinese Annals of Mathematics. Series B 1 Journal of Knot Theory and its Ramifications 1 Combinatorics, Probability and Computing 1 Bulletin des Sciences Mathématiques 1 Séminaire Lotharingien de Combinatoire 1 Annals of Combinatorics 1 Discrete Mathematics and Theoretical Computer Science. DMTCS 1 Communications in Nonlinear Science and Numerical Simulation 1 Journal of Systems Science and Complexity 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Scientia. Series A: Mathematical Sciences. New Series 1 Electronic Research Archive all top 5 Cited in 26 Fields 58 Special functions (33-XX) 46 Number theory (11-XX) 44 Combinatorics (05-XX) 35 Computer science (68-XX) 10 Quantum theory (81-XX) 8 Field theory and polynomials (12-XX) 8 Difference and functional equations (39-XX) 6 Numerical analysis (65-XX) 4 Approximations and expansions (41-XX) 3 Sequences, series, summability (40-XX) 3 Integral transforms, operational calculus (44-XX) 2 General and overarching topics; collections (00-XX) 2 Partial differential equations (35-XX) 2 Probability theory and stochastic processes (60-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Convex and discrete geometry (52-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Relativity and gravitational theory (83-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Citations by Year