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 99 articles , 1 standard article )

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  1. 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)
  2. Tabbara, R.; Owczarek, A.L.; Rechnitzer, A.: An exact solution of three interacting friendly walks in the bulk (2016)
  3. Albert, Michael; Bousquet-Mélou, Mireille: Permutations sortable by two stacks in parallel and quarter plane walks (2015)
  4. Koepf, Wolfram; Chiadjeu, Etienne Nana: Algorithmic approach for formal Fourier series (2015)
  5. Kauers, Manuel: Bounds for D-finite closure properties (2014)
  6. Beuchler, Sven; Pillwein, Veronika; Zaglmayr, Sabine: Sparsity optimized high order finite element functions for $H(\mathrmcurl)$ on tetrahedra (2013)
  7. Gerhold, Stefan; Kauers, Manuel; Koutschan, Christoph; Paule, Peter; Schneider, Carsten; Zimmermann, Burkhard: Computer-assisted proofs of some identities for Bessel functions of fractional order (2013)
  8. Kauers, Manuel: The holonomic toolkit (2013)
  9. Lorenz, William Andrew; Ponty, Yann: Non-redundant random generation algorithms for weighted context-free grammars (2013)
  10. Rosenkranz, M.; Korporal, A.: A noncommutative algebraic operational calculus for boundary problems (2013)
  11. van der Hoeven, Joris: Guessing singular dependencies (2013)
  12. Bousquet-Mélou, Mireille; Fusy, Éric; Préville-Ratelle, Louis-François: The number of intervals in the $m$-Tamari lattices (2012)
  13. Buchberger, Bruno; Rosenkranz, Markus: Transforming problems from analysis to algebra: a case study in linear boundary problems (2012)
  14. Kurkova, Irina; Raschel, Kilian: On the functions counting walks with small steps in the quarter plane (2012)
  15. Rosenkranz, Markus; Regensburger, Georg; Tec, Loredana; Buchberger, Bruno: Symbolic analysis for boundary problems: from rewriting to parametrized Gröbner bases (2012)
  16. Bernardi, Olivier; Bousquet-Mélou, Mireille: Counting colored planar maps: algebraicity results (2011)
  17. Hebisch, Waldemar; Rubey, Martin: Extended rate, more GFUN (2011)
  18. Kauers, Manuel; Zeilberger, Doron: The computational challenge of enumerating high-dimensional rook walks (2011)
  19. Bacher, Roland; Flajolet, Philippe: Pseudo-factorials, elliptic functions, and continued fractions (2010)
  20. Benoit, Alexandre; Chyzak, Frédéric; Darrasse, Alexis; Gerhold, Stefan; Mezzarobba, Marc; Salvy, Bruno: The dynamic dictionary of mathematical functions (DDMF) (2010)

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