The gfun package provides tools for determining and manipulating generating functions. You can perform computations with generating functions defined by equations. For example, given two generating functions defined by linear differential equations with polynomial coefficients, there is a procedure to compute the differential equation satisfied by their product. Each command in the gfun package can be accessed by using either the long form or the short form of the command name in the command calling sequence. As the underlying implementation of the gfun package is a module, it is also possible to use the form gfun:-command to access a command from the package. For more information, see Module Members.

References in zbMATH (referenced in 117 articles , 1 standard article )

Showing results 1 to 20 of 117.
Sorted by year (citations)

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  1. Pillwein, Veronika: On the positivity of the Gillis-Reznick-Zeilberger rational function (2019)
  2. Spiegelhofer, Lukas; Wallner, Michael: The Tu-Deng conjecture holds almost surely (2019)
  3. Barnard, Emily; Reading, Nathan: Coxeter-bicatalan combinatorics (2018)
  4. Huang, Hui; Kauers, Manuel: D-finite numbers (2018)
  5. Bacher, Axel; Bodini, Olivier; Jacquot, Alice: Efficient random sampling of binary and unary-binary trees via holonomic equations (2017)
  6. Bonichon, Nicolas; Bousquet-Mélou, Mireille; Dorbec, Paul; Pennarun, Claire: On the number of planar Eulerian orientations (2017)
  7. Bostan, Alin; Lairez, Pierre; Salvy, Bruno: Multiple binomial sums (2017)
  8. Castiglione, Giusi; Massazza, Paolo: On a class of languages with holonomic generating functions (2017)
  9. Guillén, Martha Bernal; Corey, Daniel; Donten-Bury, Maria; Fujita, Naoki; Merz, Georg: Khovanskii bases of Cox-Nagata rings and tropical geometry (2017)
  10. Oliver, Kamilla; Prodinger, Helmut: Summations in Bernoulli’s triangles via generating functions (2017)
  11. Shalosh B. Ekhad, Mingjia Yang: Automated Proofs of Many Conjectured Recurrences in the OEIS made by R.J. Mathar (2017) arXiv
  12. Bostan, Alin; Bousquet-Mélou, Mireille; Kauers, Manuel; Melczer, Stephen: On 3-dimensional lattice walks confined to the positive octant (2016)
  13. Bostan, Alin; Chèze, Guillaume; Cluzeau, Thomas; Weil, Jacques-Arthur: Efficient algorithms for computing rational first integrals and Darboux polynomials of planar polynomial vector fields (2016)
  14. Tabbara, R.; Owczarek, A. L.; Rechnitzer, A.: An exact solution of three interacting friendly walks in the bulk (2016)
  15. Albert, Michael; Bousquet-Mélou, Mireille: Permutations sortable by two stacks in parallel and quarter plane walks (2015)
  16. Kauers, Manuel; Jaroschek, Maximilian; Johansson, Fredrik: Ore polynomials in Sage (2015)
  17. Koepf, Wolfram; Chiadjeu, Etienne Nana: Algorithmic approach for formal Fourier series (2015)
  18. Shalosh B. Ekhad, N. J. A. Sloane, Doron Zeilberger: A Meta-Algorithm for Creating Fast Algorithms for Counting ON Cells in Odd-Rule Cellular Automata (2015) arXiv
  19. Kauers, Manuel: Bounds for D-finite closure properties (2014)
  20. Shalosh B. Ekhad, Doron Zeilberger: Automatic Proofs of Asymptotic ABNORMALITY (and much more!) of Natural Statistics Defined on Catalan-Counted Combinatorial Families (2014) arXiv

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