Finding all hypergeometric solutions of linear differential equations

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Finding all hypergeometric solutions of linear differential equations

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1993 international symposium on Symbolic and algebraic computation table of contents

Kiev, Ukraine

Pages: 27 - 33

Year of Publication: 1993

ISBN:0-89791-604-2

Authors

Marko Petkovšek
Bruno Salvy

Sponsor

SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 5, Downloads (12 Months): 32, Citation Count: 4

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	ABRAMOV, S. A. Problems in computer algebra that are connected with a search for polynomial solutions of linear differential and difference equations. Moscow University Compul. Math. Cybernet., 3 (1989), 63-68. Transl. from Vestn. Moskov. univ. Set. XV Vychisl. mat. kibernet. 3, 56-60.
	2	ERDI~LYI, A. Higher Transcendental Funcl~ons, second ed., vol. 1-2-3. R. E. Krieger publishing Company, Inc., Malabar, Florida, 1981.
	3	GosPEtt, l~. W. Decision procedure for indefinite hypergeometric summation. Proceedings of the National Academy of Sczences USA 75, 1 (Jan. 1978), 40-42.
	4	D. Yu. Grigor'ev, Complexity of factoring and calculating the GCD of linear ordinary differential operators, Journal of Symbolic Computation, v.10 n.1, p.7-37, July 1990 [doi>10.1016/S0747-7171(08)80034-X]
	5	Wolfram Koepf, Power series in computer algebra, Journal of Symbolic Computation, v.13 n.6, p.581-603, June 1992
	6	Marko Petkovšek, Hypergeometric solutions of linear recurrences with polynomial coefficients, Journal of Symbolic Computation, v.14 n.2-3, p.243-264, Aug./Sept. 1992 [doi>10.1016/0747-7171(92)90038-6]
	7	A_ P., BP~YC,KOV, Y. A., AND MARICHEv,PRUDNIKOV'o__I. Integrals and Series Volume 3: More special funclzons. Gordon and Breach, 1989. 800 pages. First edition in Moscow, Nauka, 1986.
	8	Bruno Salvy , Paul Zimmerman, GFUN: a Maple package for the manipulation of generating and holonomic functions in one variable, ACM Transactions on Mathematical Software (TOMS), v.20 n.2, p.163-177, June 1994 [doi>10.1145/178365.178368]
	9	Michael F. Singer, Formal solutions of differential equations, Journal of Symbolic Computation, v.10 n.1, p.59-94, July 1990 [doi>10.1016/S0747-7171(08)80037-5]
	10	STANLEY, R. P. Generating functions. In Studies in Combinatomcs, M.A.A. Studies in Mathematics, Vol. 17. (1978), G.-C. Rota, Ed., The Mathematical Association of America, pp. 100-141.
	11	Doron Zeilberger, A maple program for proving hypergeometric identities, ACM SIGSAM Bulletin, v.25 n.3, p.4-13, July 1991 [doi>10.1145/122514.122515]
	12	Doron Zeilberger, The method of creative telescoping, Journal of Symbolic Computation, v.11 n.3, p.195-204, March 1991 [doi>10.1016/S0747-7171(08)80044-2]

CITED BY 4

	Kelly Roach, Hypergeometric function representations, Proceedings of the 1996 international symposium on Symbolic and algebraic computation, p.301-308, July 24-26, 1996, Zurich, Switzerland
	Kelly Roach, Meijer G function representations, Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.205-211, July 21-23, 1997, Kihei, Maui, Hawaii, United States
	L. Chan , E. S. Cheb-Terrab, Non-liouvillian solutions for second order Linear ODEs, Proceedings of the 2004 international symposium on Symbolic and algebraic computation, p.80-86, July 04-07, 2004, Santander, Spain
	A. A. Ryabenko, Formal Solutions of Linear Ordinary Differential Equations Containing m-Hypergeometric Series, Programming and Computing Software, v.28 n.2, p.92-101, March-April 2002