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 127 articles , 1 standard article )

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  1. Bostan, A.; Krick, T.; Szanto, A.; Valdettaro, M.: Subresultants of ((x-\alpha)^m) and ((x-\beta)^n), Jacobi polynomials and complexity (2020)
  2. Giesbrecht, Mark; Haraldson, Joseph; Kaltofen, Erich: Computing approximate greatest common right divisors of differential polynomials (2020)
  3. Jiménez-Pastor, Antonio; Pillwein, Veronika; Singer, Michael F.: Some structural results on (\mathrmD^n)-finite functions (2020)
  4. Banderier, Cyril; Krattenthaler, Christian; Krinik, Alan; Kruchinin, Dmitry; Kruchinin, Vladimir; Nguyen, David; Wallner, Michael: Explicit formulas for enumeration of lattice paths: basketball and the kernel method (2019)
  5. Bendkowski, Maciej; Lescanne, Pierre: On the enumeration of closures and environments with an application to random generation (2019)
  6. Jiménez-Pastor, Antonio: DD-finite functions in Sage (2019)
  7. Jiménez-Pastor, Antonio; Pillwein, Veronika: A computable extension for D-finite functions: DD-finite functions (2019)
  8. Pillwein, Veronika: On the positivity of the Gillis-Reznick-Zeilberger rational function (2019)
  9. Salvy, Bruno: Linear differential equations as a data structure (2019)
  10. Spiegelhofer, Lukas; Wallner, Michael: The Tu-Deng conjecture holds almost surely (2019)
  11. Barnard, Emily; Reading, Nathan: Coxeter-bicatalan combinatorics (2018)
  12. Huang, Hui; Kauers, Manuel: D-finite numbers (2018)
  13. Bacher, Axel; Bodini, Olivier; Jacquot, Alice: Efficient random sampling of binary and unary-binary trees via holonomic equations (2017)
  14. Bonichon, Nicolas; Bousquet-Mélou, Mireille; Dorbec, Paul; Pennarun, Claire: On the number of planar Eulerian orientations (2017)
  15. Bostan, Alin; Lairez, Pierre; Salvy, Bruno: Multiple binomial sums (2017)
  16. Castiglione, Giusi; Massazza, Paolo: On a class of languages with holonomic generating functions (2017)
  17. Guillén, Martha Bernal; Corey, Daniel; Donten-Bury, Maria; Fujita, Naoki; Merz, Georg: Khovanskii bases of Cox-Nagata rings and tropical geometry (2017)
  18. Oliver, Kamilla; Prodinger, Helmut: Summations in Bernoulli’s triangles via generating functions (2017)
  19. Shalosh B. Ekhad, Mingjia Yang: Automated Proofs of Many Conjectured Recurrences in the OEIS made by R.J. Mathar (2017) arXiv
  20. Bostan, Alin; Bousquet-Mélou, Mireille; Kauers, Manuel; Melczer, Stephen: On 3-dimensional lattice walks confined to the positive octant (2016)

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