The gfun package

Gfun is a Maple package that provides tools for

  • guessing a sequence or a series from its first terms;

  • manipulating rigorously solutions of linear differential or recurrence equations, using the equation as a data-structure.

Latest version

 gfun 3.76 (July 2015). Once downloaded, see the help page of libname to understand how to make them available from Maple. Typically, your session will contain something like libname:="gfun_path",libname:

You can check that this worked by asking gfun:-version(); that should return the number above.

The source code can be read by anyone who can read Maple code, but if you want to use the package, then it’s better to download it with the link above.

Help pages

All the help pages are available directly from within Maple, and here are pdf versions:

Reference for gfun

The primary reference to use when citing gfun is the following one:

B. Salvy and P. Zimmermann, “Gfun: a Maple package for the manipulation of generating and holonomic functions in one variable,” toms, vol. 20, no. 2, pp. 163–177, 1994.

If you are using the NumGfun subpackage, then the proper reference is:

M. Mezzarobba, “NumGfun: a Package for Numerical and Analytic Computation with D-finite Functions,” in Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation (ISSAC 2010), 2010, pp. 139–145.

Articles citing gfun

The following is a list of articles that cite gfun. If you know of an article that is not in this list, but does cite gfun, please send me an email so that I can add it to this list.

2016

  • A. Bostan, G. Chèze, T. Cluzeau, and J.-A. Weil, “Efficient algorithms for computing rational first integrals and darboux polynomials of planar polynomial vector fields,” Mathematics of Computation, vol. 85, no. 299, pp. 1393–1425, 2016.

2015

  • M. Albert and M. Bousquet-Mélou, “Permutations sortable by two stacks in parallel and quarter plane walks,” European J. Combin., vol. 43, pp. 131–164, 2015.

2014

  • M. Kauers, “Bounds for D-finite Closure Properties,” in Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, New York, NY, USA, 2014, pp. 288–295.
  • W. Y. C. Chen, Q.-H. Guo, L. H. Sun, and J. Wang, “Zigzag Stacks and m-Regular Linear Stacks,” Journal of Computational Biology, vol. 21, no. 12, pp. 915–935, 2014.

2013

  • W. A. Lorenz and Y. Ponty, “Non-redundant random generation algorithms for weighted context-free grammars,” Theoretical Computer Science, vol. 502, pp. 177–194, 2013.
  • K. Dias, “Enumerating combinatorial classes of the complex polynomial vector fields in \mathbb C,” Ergodic Theory and Dynamical Systems, vol. 33, no. 2, pp. 416–440, 2013.
  • T. Combot, “Integrability conditions at order 2 for homogeneous potentials of degree -1,” Nonlinearity, vol. 26, no. 1, pp. 95–120, 2013.
  • S. Beuchler, V. Pillwein, and S. Zaglmayr, “Sparsity optimized high order finite element functions for on tetrahedra,” Advances in Applied Mathematics, vol. 50, no. 5, pp. 749–769, 2013.

2012

  • M. Elder, A. Rechnitzer, and T. Wong, “On the cogrowth of Thompson’s group F,” Groups, Complexity, Cryptology, vol. 4, no. 2, pp. 301–320, 2012.
  • B. Buchberger and M. Rosenkranz, “Transforming problems from analysis to algebra: A case study in linear boundary problems,” Journal of Symbolic Computation, vol. 47, no. 6, pp. 589–609, 2012.
  • N. Brisebarre et al., “Rigorous polynomial approximation using Taylor models in Coq,” 2012, vol. 7226 LNCS, pp. 85–99.
  • M. Bousquet-Mélou, E. Fusy, and L.-. Préville-Ratelle, “The number of intervals in the m-Tamari lattices,” Electronic Journal of Combinatorics, vol. 18, no. 2, pp. 1–26, 2012.

2011

  • G. Labelle and A. Lacasse, “Closed paths whose steps are roots of unity,” in FPSAC’11 - 23rd International Conference on Formal Power Series and Algebraic Combinatorics, 2011, pp. 599–610.
  • M. Kauers, “The concrete tetrahedron,” in Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, 2011, p. 7.
  • W. Hebisch and M. Rubey, “Extended rate, more GFUN,” Journal of Symbolic Computation, vol. 46, no. 8, pp. 889–903, 2011.
  • A. Bostan, F. Chyzak, Z. Li, and B. Salvy, “Fast computation of common left multiples of linear ordinary differential operators,” ACM Communications in Computer Algebra, vol. 45, no. 1-2, pp. 111–112, 2011.
  • O. Bernardi and M. Bousquet-Mélou, “Counting colored planar maps: Algebraicity results,” Journal of Combinatorial Theory.Series B, vol. 101, no. 5, pp. 315–377, 2011.
  • A. Al-Salman, M. B. H. Rhouma, and A. A. Al-Jarrah, “On integrals and sums involving special functions,” Missouri Journal of Mathematical Sciences, vol. 23, no. 2, pp. 123–141, 2011.

2010

  • M. Mezzarobba, “NumGfun: a Package for Numerical and Analytic Computation with D-finite Functions,” in Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation (ISSAC 2010), 2010, pp. 139–145.
  • M. Mezzarobba and B. Salvy, “Effective bounds for P-recursive sequences,” Journal of Symbolic Computation, vol. 45, no. 10, pp. 1075–1096, 2010.
  • A. Denise, Y. Ponty, and M. Termier, “Controlled non-uniform random generation of decomposable structures,” Theoretical Computer Science, vol. 411, no. 40-42, pp. 3527–3552, 2010.
  • A. Bostan, B. Salvy, and K. Tran, “Generating functions of Chebyshev-like polynomials,” International Journal of Number Theory, vol. 6, no. 7, pp. 1659–1667, 2010.
  • A. Bostan, M. Kauers, and M. V. Hoeij, “The complete generating function for gessel walks is algebraic,” Proceedings of the American Mathematical Society, vol. 138, no. 9, pp. 3063–3078, 2010.
  • A. Benoit, F. Chyzak, A. Darrasse, S. Gerhold, M. Mezzarobba, and B. Salvy, “The Dynamic Dictionary of Mathematical Functions (DDMF),” 2010, vol. 6327 LNCS, pp. 35–41.
  • R. Bacher and P. Flajolet, “Pseudo-factorials, elliptic functions, and continued fractions,” Ramanujan Journal, vol. 21, no. 1, pp. 71–97, 2010.

2009

  • J. van der Hoeven, “On asymptotic extrapolation,” Journal of Symbolic Computation, vol. 44, no. 8, pp. 1000–1016, 2009.
  • A. Rechnitzer, “The anisotropic generating function of self-avoiding polygons is not d-finite,” 2009, vol. 775, pp. 93–115.
  • P.-. Koseleff and D. Pecker, “A polynomial parametrization of torus knots,” Applicable Algebra in Engineering, Communications and Computing, vol. 20, no. 5-6, pp. 361–377, 2009.
  • M. Kauers and C. Koutschan, “A Mathematica package for q-holonomic sequences and power series,” Ramanujan Journal, vol. 19, no. 2, pp. 137–150, 2009.
  • S. Gerhold and R. Warnung, “Finding efficient recursions for risk aggregation by computer algebra,” Journal of Computational and Applied Mathematics, vol. 223, no. 1, pp. 499–507, 2009.
  • P. L. Douillet, “Sampling distribution of the variance,” in Proceedings - Winter Simulation Conference, 2009, pp. 403–414.
  • W. Y. C. Chen, H. S. W. Han, and C. M. Reidys, “Random k-noncrossing RNA structures,” Proceedings of the National Academy of Sciences of the United States of America, vol. 106, no. 52, pp. 22061–22066, 2009.
  • A. Bostan and M. Kauers, “Automatic classification of restricted lattice walks,” in FPSAC’09 - 21st International Conference on Formal Power Series and Algebraic Combinatorics, 2009, pp. 201–215.
  • J. Blümlein, M. Kauers, S. Klein, and C. Schneider, “Determining the closed forms of the O (as 3) anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra,” Computer Physics Communications, vol. 180, no. 11, pp. 2143–2165, 2009.

2008

  • J. Zhang, “Sumudu transform based coefficients calculation,” Nonlinear Studies, vol. 15, no. 4, pp. 355–372, 2008.
  • N. R. Rao and A. Edelman, “The polynomial method for random matrices,” Foundations of Computational Mathematics, vol. 8, no. 6, pp. 649–702, 2008.
  • H. Prodinger, “On the order of the recursion relation of Motzkin numbers of higher rank,” Open Appl. Math. J., vol. 2, pp. 14–15, 2008.
  • Y. Ponty, “Efficient sampling of RNA secondary structures from the Boltzmann ensemble of low-energy : Ttthe boustrophedon method,” Journal of mathematical biology, vol. 56, no. 1-2, pp. 107–127, 2008.
  • W. A. Lorenz, Y. Ponty, and P. Clote, “Asymptotics of RNA shapes,” Journal of Computational Biology, vol. 15, no. 1, pp. 31–63, 2008.
  • M. Kauers and B. Zimmermann, “Computing the algebraic relations of C-finite sequences and multisequences,” Journal of Symbolic Computation, vol. 43, no. 11, pp. 787–803, 2008.
  • S. Gerhold, L. Glebsky, C. Schneider, H. Weiss, and B. Zimmermann, “Computing the complexity for Schelling segregation models,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 10, pp. 2236–2245, 2008.
  • G. P. Egorychev and E. V. Zima, “Integral Representation and Algorithms for Closed Form Summation,” vol. 5, M. Hazewinkel, Ed. North-Holland, 2008, pp. 459–529.
  • J. Carette, S. Smith, J. McCutchan, C. Anand, and A. Korobkine, “Case studies in model manipulation for scientific computing,” 2008, vol. 5144 LNAI, pp. 24–37.
  • J. M. Borwein and B. Salvy, “A proof of a recursion for Bessel moments,” Experimental Mathematics, vol. 17, no. 2, pp. 223–230, 2008.
  • O. Bernardi, “On triangulations with high vertex degree,” Annals of Combinatorics, vol. 12, no. 1, pp. 17–44, 2008.
  • A. Ayyer and D. Zeilberger, “Two dimensional directed lattice walks with boundaries,” in Tapas in experimental mathematics, vol. 457, Providence, RI: Amer. Math. Soc., 2008, pp. 1–19.

2007

  • D. Zeilberger, “The Holonomic Ansatz II. Automatic discovery(!) and proof(!!) of holonomic determinant evaluations,” Annals of Combinatorics, vol. 11, no. 2, pp. 241–247, 2007.
  • C. Schneider, “Symbolic summation assists combinatorics,” Séminaire Lotharingien de Combinatoire, vol. 56, no. B56b, pp. 1–36, 2007.
  • C. Schneider, “Apéry’s double sum is plain sailing indeed,” Electronic Journal of Combinatorics, vol. 14, no. 1 N, pp. 1–3, 2007.
  • P. Paule and C. Schneider, “Truncating Binomial Series with Symbolic Summation,” INTEGERS. Electronic Journal of Combinatorial Number Theory, vol. 7, no. A22, pp. 1–9, 2007.
  • T. Mansour, M. Schork, and Y. Sun, “Motzkin numbers of higher rank: Generating function and explicit expression,” Journal of Inequalities in Pure and Applied Mathematics, vol. 8, no. 2, 2007.
  • L. Kovács, N. Popov, and T. Jebelean, “Combining logic and algebraic techniques for program verification in Theorema,” in Proceedings - ISoLA 2006: 2nd International Symposium on Leveraging Applications of Formal Methods, Verification and Validation, 2007, pp. 67–74.
  • W. Koepf, P. M. Rajkovic, and S. D. Marinkovic, “Properties of q-holonomic functions,” Journal of Difference Equations and Applications, vol. 13, no. 7, pp. 621–638, 2007.
  • W. Koepf, “Bieberbach’s conjecture, the de Branges and Weinstein functions and the Askey-Gasper inequality,” Ramanujan Journal, vol. 13, no. 1-3, pp. 103–129, 2007.
  • M. Kauers, “An algorithm for deciding zero equivalence of nested polynomially recurrent sequences,” ACM Transactions on Algorithms, vol. 3, no. 2, 2007.
  • M. Kauers, “Computer algebra and power series with positive coefficients,” in FPSAC’07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics, 2007.
  • É. Fusy, “Counting Unrooted Maps Using Tree-Decomposition,” Séminaire Lotharingien de Combinatoire, vol. 54A, pp. 1–44, 2007.
  • J. Carette and R. Janicki, “Computing properties of numerical imperative programs by symbolic computation,” Fundamenta Informaticae, vol. 80, no. 1-3, pp. 125–146, 2007.
  • M. Bodirsky, C. Gröpl, D. Johannsen, and M. Kang, “A direct decomposition of 3-connected planar graphs,” Séminaire Lotharingien de Combinatoire, vol. 54a, no. B54Ak, pp. 1–15, 2007.

2006

  • T. C. Scott, M. Aubert-Frécon, and J. Grotendorst, “New approach for the electronic energies of the hydrogen molecular ion,” Chemical Physics, vol. 324, no. 2-3, pp. 323–338, 2006.
  • A. Rechnitzer, “Haruspicy 3: The anisotropic generating function of directed bond-animals is not D-finite,” Journal of Combinatorial Theory.Series A, vol. 113, no. 6, pp. 1031–1049, 2006.
  • P. Massazza and R. Radicioni, “A symbolic approach to computing the holonomic functions,” Pure Mathematics and Applications, vol. 17, no. 1-2, pp. 147–164, 2006.
  • M. Kauers, “Shift equivalence of P-finite sequences,” Electronic Journal of Combinatorics, vol. 13, no. 1 R, pp. 1–16, 2006.
  • S. Gerhold and M. Kauers, “A computer proof of Turán’s inequality,” Journal of Inequalities in Pure and Applied Mathematics, vol. 7, no. 2, pp. 1–4, 2006.
  • M. Bousquet-Mélou, “Rational and algebraic series in combinatorial enumeration,” in International Congress of Mathematicians. Vol. III, Eur. Math. Soc., Zürich, 2006, pp. 789–826.
  • M. Bousquet-Mélou and G. Xin, “On Partitions Avoiding 3-Crossings,” Séminaire Lotharingien de Combinatoire, vol. B54e, pp. 1–21, 2006.
  • M. Bousquet-Mélou, “Three osculating walkers,” Journal of Physics: Conference Series, vol. 42, no. 1, pp. 35–46, 2006.
  • A. Bećirović, P. Paule, V. Pillwein, A. Riese, C. Schneider, and J. Schöberl, “Hypergeometric summation algorithms for high-order finite elements,” Computing (Vienna/New York), vol. 78, no. 3, pp. 235–249, 2006.

2005

  • F. Ulmer, “Note on algebraic solutions of differential equations with known finite Galois group,” Applicable Algebra in Engineering, Communications and Computing, vol. 16, no. 4, pp. 205–218, 2005.
  • B. Salvy, “D-finiteness: Algorithms and applications,” in Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, 2005, vol. 2005, pp. 2–3.
  • E. Fusy, “Counting unrooted maps using tree-decomposition,” in FPSAC Proceedings 2005 - 17th Annual International Conference on Formal Power Series and Algebraic Combinatorics, 2005, pp. 123–134.
  • F. Chyzak, M. Mishna, and B. Salvy, “Effective scalar products of D-finite symmetric functions,” Journal of Combinatorial Theory.Series A, vol. 112, no. 1, pp. 1–43, 2005.
  • M. Bousquet-Mélou, “Algebraic generating functions in enumerative combinatorics and context-free languages,” in Lecture Notes in Computer Science, 2005, vol. 3404, pp. 18–35.
  • M. Bodirsky, C. Gröpl, D. Johannsen, and M. Kang, “A direct decomposition of 3-connected planar graphs,” in FPSAC Proceedings 2005 - 17th Annual International Conference on Formal Power Series and Algebraic Combinatorics, 2005, pp. 459–470.
  • G. E. Andrews, P. Paule, and C. Schneider, “Plane partitions VI: Stembridge’s TSPP theorem,” Advances in Applied Mathematics, vol. 34, no. 4 SPEC. ISS., pp. 709–739, 2005.

2004

  • C. Schneider, “The summation package Sigma: Underlying principles and a rhombus tiling application,” Discrete Mathematics and Theoretical Computer Science, vol. 6, no. 2, pp. 365–386, 2004.
  • M. Foupouagnigni, W. Koepf, and A. Ronveaux, “Factorization of fourth-order differential equations for perturbed classical orthogonal polynomials,” Journal of Computational and Applied Mathematics, vol. 162, no. 2, pp. 299–326, 2004.
  • M. Ahmed, R. Ward, and N. Kharma, “Solving mathematical problems using knowledge-based systems,” Mathematics and Computers in Simulation, vol. 67, no. 1-2, pp. 149–161, 2004.

2003

  • N. J. A. Sloane, “The on-line encyclopedia of integer sequences,” Notices of the AMS, vol. 50, no. 8, pp. 912–915, 2003.
  • P. Paule and C. Schneider, “Computer proofs of a new family of harmonic number identities,” Advances in Applied Mathematics, vol. 31, no. 2, pp. 359–378, 2003.
  • L. Meunier and B. Salvy, “ESF: An Automatically Generated Encyclopedia of Special Functions,” in Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, 2003, pp. 199–206.
  • W. Koepf, “Computer algebra algorithms for orthogonal polynomials and special functions,” in Orthogonal polynomials and special functions (Leuven, 2002), vol. 1817, Berlin: Springer, 2003, pp. 1–24.
  • M. Foupouagnigni, W. Koepf, and A. Ronveaux, “On fourth-order difference equations for orthogonal polynomials of a discrete variable: Derivation, factorization and solutions,” Journal of Difference Equations and Applications, vol. 9, no. 9, pp. 777–804, 2003.
  • M. Durand, “Asymptotic analysis of an optimized quicksort algorithm,” Information Processing Letters, vol. 85, no. 2, pp. 73–77, 2003.
  • C. A. C. Brennan and H. Prodinger, “The pills problem revisited,” Quaestiones Mathematicae, vol. 26, no. 4, pp. 427–439, 2003.
  • M. Barkatou, F. Chyzak, and M. Loday-Richaud, “Remarques algorithmiques liées au rang d’un opérateur différentiel linéaire,” in From Combinatorics to Dynamical Systems (Journées de Calcul Formel, Strasbourg, March 22-23, 2002), 2003, vol. 3, p. 87—129.

2002

  • J. Van der Hoeven, “Relax, but don’t be too lazy,” Journal of Symbolic Computation, vol. 34, no. 6, pp. 479–542, 2002.
  • P. Nicodème, B. Salvy, and P. Flajolet, “Motif statistics,” Theoretical Computer Science, vol. 287, no. 2, pp. 593–617, 2002.
  • A. J. Guttmann and M. Vöge, “Lattice paths: vicious walkers and friendly walkers,” Journal of Statistical Planning and Inference, vol. 101, no. 1-2, pp. 107–131, 2002.
  • P. Flajolet, K. Hatzis, S. Nikoletseas, and P. Spirakis, “On the robustness of interconnections in random graphs: A symbolic approach,” Theoretical Computer Science, vol. 287, no. 2, pp. 515–534, 2002.
  • B. R. Fabijonas, “Laplace’s method on a computer algebra system with an application to the real valued modified Bessel functions,” Journal of Computational and Applied Mathematics, vol. 146, no. 2, pp. 323–342, 2002.
  • E. Deutsch and M. Noy, “Statistics on non-crossing trees,” Discrete Mathematics, vol. 254, no. 1-3, pp. 75–87, 2002.
  • C. Banderier and P. Flajolet, “Basic analytic combinatorics of directed lattice paths,” Theoretical Computer Science, vol. 281, no. 1-2, pp. 37–80, 2002.

2001

  • B. Beckermann and G. Labahn, “Fraction-free computation of matrix rational interpolants and matrix GCDs,” SIAM Journal on Matrix Analysis and Applications, vol. 22, no. 1, pp. 114–144, 2001.

2000

  • R. Suter, “Two analogues of a classical sequence,” Journal of Integer Sequences, vol. 3, no. 1, pp. 1–18, 2000.
  • B. Litow, “On Hadamard square roots of unity,” Theoretical Computer Science, vol. 237, no. 1-2, pp. 447–454, 2000.
  • R. Lercier and F. Morain, “Computing isogenies between elliptic curves over Fp n using Couveignes’s algorithm,” Mathematics of Computation, vol. 69, no. 229, pp. 351–370, 2000.
  • M. Fulmek and C. Krattenthaler, “The Number of Rhombus Tilings of a Symmetric Hexagon which Contain a Fixed Rhombus on the Symmetry Axis, II,” European Journal of Combinatorics, vol. 21, no. 5, pp. 601–640, 2000.
  • E. Deutsch and M. Noy, “New statistics on non-crossing trees,” in Formal power series and algebraic combinatorics (Moscow, 2000), Berlin: Springer, 2000, pp. 667–676.
  • S. Brogelli, D. Merlini, and R. Sprugnoli, “Proving a class of hypergeometric identities by means of generating functions,” in Formal power series and algebraic combinatorics (Moscow, 2000), Berlin: Springer, 2000, pp. 645–654.
  • M. Bousquet-Mélou, “Sorted and/or sortable permutations,” Discrete Mathematics, vol. 225, no. 1-3, pp. 25–50, 2000.
  • F. Bergeron and F. Gascon, “Counting young tableaux of bounded height,” Journal of Integer Sequences, vol. 3, no. 1, pp. 1–7, 2000.
  • B. Beckermann and G. Labahn, “Effective Computation of Rational Approximants and Interpolants,” Reliable Computing, vol. 6, no. 4, pp. 365–390, 2000.

1999

  • A. Ronveaux, A. Zarzo, I. Area, and E. Godoy, “Decomposition of polynomials with respect to the cyclic group of order m,” J. Symbolic Comput., vol. 28, no. 6, pp. 755–765, 1999.
  • C. Krattenthaler, “Advanced determinant calculus,” Séminaire Lotharingien de Combinatoire, vol. 42, pp. 1–67, 1999.
  • W. Koepf, “Software for the algorithmic work with orthogonal polynomials and special functions,” Electronic Transactions on Numerical Analysis, vol. 9, pp. 77–101, 1999.
  • P. Flajolet and M. Noy, “Analytic combinatorics of non-crossing configurations,” Discrete Mathematics, vol. 204, no. 1-3, pp. 203–229, 1999.
  • R. Evans, H. D. L. Hollmann, C. Krattenthaler, and Q. Xiang, “Gauss Sums, Jacobi Sums, and p-Ranks of Cyclic Difference Sets,” Journal of Combinatorial Theory.Series A, vol. 87, no. 1, pp. 74–119, 1999.
  • A. Denise and P. Zimmermann, “Uniform random generation of decomposable structures using floating-point arithmetic,” Theoretical Computer Science, vol. 218, no. 2, pp. 233–248, 1999.
  • F. Chyzak, I. Gutman, and P. Paule, “Predicting the number of hexagonal systems with 24 and 25 hexagons,” Match, vol. 40, pp. 139–151, 1999.

1998

  • A. Panholzer and H. Prodinger, “Towards a More Precise Analysis of an Algorithm to Generate Binary Trees: A Tutorial,” Computer journal, vol. 41, no. 3, pp. 201–204, 1998.
  • Martı́nez C., A. Panholzer, and H. Prodinger, “On the number of descendants and ascendants in random search trees,” Electronic Journal of Combinatorics, vol. 5, no. 1, 1998.
  • C. Krattenthaler, “An alternative evaluation of the Andrews-Burge determinant,” in Mathematical essays in honor of Gian-Carlo Rota (Cambridge, MA, 1996), vol. 161, Boston, MA: Birkhäuser Boston, 1998, pp. 263–270.
  • A. Denise, I. Dutour, and P. Zimmermann, “CS: a MuPAD Package for Counting and Randomly Generating Combinatorial Structures,” in Formal Power Series and Algebraic Combinatorics, 1998, pp. 1–10.
  • F. Chyzak and B. Salvy, “Non-commutative elimination in ore algebras proves multivariate identities,” Journal of Symbolic Computation, vol. 26, no. 2, pp. 187–227, 1998.
  • M. Bousquet-Mélou, “Multi-statistic enumeration of two-stack sortable permutations,” Electronic Journal of Combinatorics, vol. 5, no. 1, 1998.

1997

  • S. P. Tsarev, “Symbolic manipulation of integrodifferential expressions and factorization of linear ordinary differential operators over transcendental extensions of a differential field,” in ISSAC ’97: Proceedings of the 1997 international symposium on Symbolic and algebraic computation, New York, NY, USA, 1997, pp. 310–315.
  • H. Prodinger, “On a question of Cooper and Kennedy,” Fibonacci Quart., vol. 35, no. 2, pp. 135–136, 1997.
  • R. B. Pelz and Y. Gulak, “Evidence for a real-time singularity in hydrodynamics from time series analysis,” Physical Review Letters, vol. 79, no. 25, pp. 4998–5001, 1997.
  • Z. Li and I. Nemes, “A modular algorithm for computing greatest common right divisors of Ore polynomials,” in ISSAC ’97: Proceedings of the 1997 international symposium on Symbolic and algebraic computation, New York, NY, USA, 1997, pp. 282–289.
  • W. Koepf, “Identities for families of orthogonal polynomials and special functions,” Integral Transforms and Special Functions, vol. 5, no. 1-2, pp. 69–102, 1997.
  • P. Flajolet and B. Salvy, “The SIGSAM Challenges: Symbolic Asymptotics in Practice,” SIGSAM Bulletin, vol. 31, no. 4, pp. 36–47, Dec. 1997.
  • M. Bousquet-Mélou and A. J. Guttmann, “Enumeration of Three-dimensional Convex Polygons,” Annals of Combinatorics, vol. 1, no. 1, pp. 27–53, 1997.
  • S. A. Abramov and E. V. Zima, “Minimal completely factorable annihilators,” in ISSAC ’97: Proceedings of the 1997 international symposium on Symbolic and algebraic computation, New York, NY, USA, 1997, pp. 290–297.

1996

  • D. Zeilberger, “Self-avoiding walks, the language of science, and Fibonacci numbers,” Journal of Statistical Planning and Inference, vol. 54, no. 1, pp. 135–138, 1996.
  • J. Noonan and D. Zeilberger, “The enumeration of permutations with a prescribed number of ‘forbidden’ patterns,” Advances in Applied Mathematics, vol. 17, no. 4, pp. 381–407, 1996.
  • R. W. Grosse-Kunstleve, G. O. Brunner, and N. J. A. Sloane, “Algebraic description of coordination sequences and exact topological densities for zeolites,” Acta Crystallographica Section A: Foundations of Crystallography, vol. 52, no. 6, pp. 879–889, 1996.

1995

  • P. Paule and M. Schorn, “A Mathematica Version of Zeilberger’s Algorithm for Proving Binomial Coefficient Identities,” jsc, vol. 20, no. 5/6, pp. 673–698, 1995.
  • I. Nemes and M. Petkovšek, “\tt RComp: A \sl Mathematica\/ Package for Computing with Recursive Sequences,” jsc, vol. 20, no. 5/6, pp. 745–753, 1995.
  • P. Flajolet and B. Salvy, “Computer Algebra Libraries for Combinatorial Structures,” jsc, vol. 20, no. 5-6, pp. 653–671, 1995.
  • F. Bergeron and U. Sattler, “Constructible differentially finite algebraic series in several variables,” Theoretical Computer Science, vol. 144, no. 1-2, pp. 59–65, Jun. 1995.

1994

  • V. Strehl, “Binomial identities – combinatorial and algorithmic aspects,” Discrete Mathematics, vol. 136, no. 1-3, pp. 309–346, 1994.

1993

  • M. Petkovšek and B. Salvy, “Finding all hypergeometric solutions of linear differential equations,” in ISSAC’93, New York, 1993, pp. 27–33.

1992

  • F. Bergeron and S. Plouffe, “Computing the Generating Function of a Series given its First Terms,” expm, vol. 1, no. 4, pp. 308–312, 1992.