Abstract
We describe the GFUN package which contains functions for manipulating sequences, linear recurrences, or differential equations and generating functions of various types. This article is intended both as an elementary introduction to the subject and as a reference manual for the package.
- BERGERON, F. AND PLOUFFE, S. 1992. Computing the generating function of a series given its first terms. J. Exp. Math. 1, 4, 308 312,Google Scholar
- BOREL, E. 1901. Leqons sur les s~ries divergentes. In Collectwn de monograph~es sur la thdorie des fonctions, pubh& sous la &rectzon de M. Y~mde Borel. Gauthiers-Villars, Pans. Second ed. 1928 Reprinted by J. Gabay, 1988.Google Scholar
- CANDELPERGHER, B. 1989. Une introduction h la r~surgence. Gazette des Mathdmaticiens 42 (Oct.), 36-64.Google Scholar
- CHUDNOVSKY, D. V. AND CHUDNOVSKY, G.V. 1987. On expansion of algebraic functions in power and Puiseux series, II. J. Complex. 3, 1, 1-25. Google Scholar
- CHUDNOVSKY, n. V. AND CHUDNOVSKY, G.V. 1986. On expansion of algebraic functions in power and Puiseux series, I. J. Complex. 2, 4, 271-294. Google Scholar
- COMTET, L. 1974. Advanced Combinatorics. Reidel, Dordrecht, The Netherlands.Google Scholar
- COMTET, L. 1964. Calcul pratique des coefficients de Taylor d'une fonction alg~brique. L'Enseignement Mathdmatique 10,267-270.Google Scholar
- DELEST, M.-P. AND VIENNOT, G. 1984. Algebraic languages and polyominoes enumeration. Theor. Comput. Sct. 34, 1-2, 169-206.Google Scholar
- DUVAL, D. 1987. Diverses questions relatives au calcul formel avec des nombres alg~briques. Doctorat d'l~tat, Universit~ scientifique, technologique et m~dicale de Grenoble.Google Scholar
- GOURDON, X. AND SALVY, B. 1992. Asymptotics of linear recurrences with rational coefficients. Tech. Rep., INRIA, Le Chesnay Cedex, France.Google Scholar
- GRAHAM, R., KNUTH, D., AND PATASHNIK, O. 1989. Concrete Mathematics. Addison Wesley, Reading, Mass. Google Scholar
- GUTTMANN, A. J. AND ENTING, I.G. 1988. The number of convex polygons on the square and honeycomb lattices. J. Phys. A 21,467-474.Google Scholar
- LIPSHITZ, L. 1989. D-finite power series. J. Alg. 122, 2, 353-373.Google Scholar
- LODAY-RICHAUD, M. 1990. Introduction ~ la multisommabilit6. Gazette des Math~matie~ens 44, 41-63.Google Scholar
- MALGRANGE, B. AND RAMIS, J.-P, 1992. Fonctions mu}tisommables. Annales de l'lnstitut Fourier 42, 1-2, 353-368.Google Scholar
- SLOANE, N. J. A, 1973. A Handbook of Integer Sequences. Academic Press, New York.Google Scholar
- STANLEY, R.P. 1980. Differentiably finite power series. Eur. J. Combinatorics 1,175-188.Google Scholar
- THOMANN, J. 1990. Resommation des s6ries formelles. Solutions d'~quations diff~rentielles lin6aires du second ordre dans }e champ complexe au voisinage de singularities irr~guli~res. Numer. Math. 58, 5, 503-535.Google Scholar
- ULMER, F. 1991. On algebraic solutions of linear differential equations with primitive unimodular Galois group. In Algebraic Algortthms and Error Correcting Codes. Lecture Notes in Computer Science, vol. 307. Springer-Verlag, Berlin, 446-455. Google Scholar
- WASOW, W. 1987. Asymptotic Expansions for Ordinary Differenttal Equattons. Dover, New York, 1965.Google Scholar
- WmF, H.S. 1990. Generatingfuncttonology. Academic Press, New York.Google Scholar
- ZEILBERGER, n. 1992. A proof of Julian West's conjecture that the number of two-stack-sorta-ble permutations of length n is 2(3n)!/((n + 1)!(2n + 1)!). Dtsc. Math. 102, 1, 85 93. Google Scholar
- ZEmBERGER, D. 1990. A holonomlc systems approach to special functions identities. J. Cornput. Appl. Math. 32, 3, 321-368. Google Scholar
Index Terms
- GFUN: a Maple package for the manipulation of generating and holonomic functions in one variable
Recommendations
D-finiteness: algorithms and applications
ISSAC '05: Proceedings of the 2005 international symposium on Symbolic and algebraic computationDifferentially finite series are solutions of linear differential equations with polynomial coefficients. P-recursive sequences are solutions of linear recurrences with polynomial coefficients. Corresponding notions are obtained by replacing classical ...
Fast algorithms for polynomial solutions of linear differential equations
ISSAC '05: Proceedings of the 2005 international symposium on Symbolic and algebraic computationWe investigate polynomial solutions of homogeneous linear differential equations with coefficients that are polynomials with integer coefficients. The problems we consider are the existence of nonzero polynomial solutions, the determination of the ...
Low complexity algorithms for linear recurrences
ISSAC '06: Proceedings of the 2006 international symposium on Symbolic and algebraic computationWe consider two kinds of problems: the computation of polynomial and rational solutions of linear recurrences with coefficients that are polynomials with integer coefficients; indefinite and definite summation of sequences that are hypergeometric over ...
Comments