-
1
-
-
0010088447
-
The method of differentiating under the integral sign
-
Almkvist, G., Zeilberger, D. (1990). The method of differentiating under the integral sign. J. Symb. Comput., 10, 571-591.
-
(1990)
J. Symb. Comput.
, vol.10
, pp. 571-591
-
-
Almkvist, G.1
Zeilberger, D.2
-
3
-
-
0003204425
-
Gröbner bases
-
Springer Verlag. A computational approach to commutative algebra (in cooperation with Heinz Kredel)
-
Becker, T., Weispfenning, V. (1993). Gröbner bases, volume 141 of Graduate Texts in Mathematics. Springer Verlag. A computational approach to commutative algebra (in cooperation with Heinz Kredel).
-
(1993)
Graduate Texts in Mathematics
, vol.141
-
-
Becker, T.1
Weispfenning, V.2
-
4
-
-
0002993019
-
Modules over a ring of differential operators, study of the fundamental solutions of equations with constant coefficients
-
(Russian); 89-101 (English translation)
-
Bernstein, I. N. (1971). Modules over a ring of differential operators, study of the fundamental solutions of equations with constant coefficients. Fund. Anal. Appl., 5, 1-16 (Russian); 89-101 (English translation).
-
(1971)
Fund. Anal. Appl.
, vol.5
, pp. 1-16
-
-
Bernstein, I.N.1
-
5
-
-
0001620260
-
The analytic continuation of generalized functions with respect to a parameter
-
(Russian); 273-285 (English translation)
-
Bernstein, I. N. (1972). The analytic continuation of generalized functions with respect to a parameter. Fund. Anal. Appl., 6, 26-40 (Russian); 273-285 (English translation).
-
(1972)
Fund. Anal. Appl.
, vol.6
, pp. 26-40
-
-
Bernstein, I.N.1
-
7
-
-
33646925446
-
Ein algorithmisches kriterium für die lösbarkeit eines algebraischen gleichungssystems
-
Buchberger, B. (1970). Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems. Aequationes Math., 4, 374-383.
-
(1970)
Aequationes Math.
, vol.4
, pp. 374-383
-
-
Buchberger, B.1
-
8
-
-
0002803133
-
Gröbner bases: An algorithmic method in polynomial ideal theory
-
Bose, N. K., ed. D. Reidel Publishing Company
-
Buchberger, B. (1985). Gröbner bases: an algorithmic method in polynomial ideal theory. In Bose, N. K., ed., Recent Trends in Multidimensional System Theory, pp. 184-232. D. Reidel Publishing Company.
-
(1985)
Recent Trends in Multidimensional System Theory
, pp. 184-232
-
-
Buchberger, B.1
-
9
-
-
0002499459
-
Démonstration "automatique" d'identités et fonctions hypergéométriques
-
Séminaire Bourbaki
-
Cartier, P. (1992). Démonstration "automatique" d'identités et fonctions hypergéométriques. Astérisque, 206, 41-91. Séminaire Bourbaki.
-
(1992)
Astérisque
, vol.206
, pp. 41-91
-
-
Cartier, P.1
-
10
-
-
0010093331
-
-
Research Report 2371, Institut National de Recherche en Informatique et en Automatique
-
Chyzak, F. (1994). Holonomic Systems and Automatic Proofs of Identities. Research Report 2371, Institut National de Recherche en Informatique et en Automatique.
-
(1994)
Holonomic Systems and Automatic Proofs of Identities
-
-
Chyzak, F.1
-
11
-
-
0010194272
-
An extension of Zeilberger's fast algorithm to general holonomic functions
-
Universität Wien
-
Chyzak, F. (1997). An extension of Zeilberger's fast algorithm to general holonomic functions. In Formal Power Series and Algebraic Combinatorics, 9th Conference, pp. 172-183. Universität Wien.
-
(1997)
Formal Power Series and Algebraic Combinatorics, 9th Conference
, pp. 172-183
-
-
Chyzak, F.1
-
12
-
-
85030049293
-
-
PhD These. Ecole polytechnique
-
Chyzak, F. (1998). PhD These. Ecole polytechnique.
-
(1998)
-
-
Chyzak, F.1
-
13
-
-
0004118933
-
-
Number 2 in London Mathematical Society Monographs. Academic Press
-
Cohn, P. M. (1971). Free Rings and Their Relations. Number 2 in London Mathematical Society Monographs. Academic Press.
-
(1971)
Free Rings and Their Relations
-
-
Cohn, P.M.1
-
14
-
-
0000503358
-
Calcul pratique des coefficients de Taylor d'une fonction algébrique
-
Comtet, L. (1964). Calcul pratique des coefficients de Taylor d'une fonction algébrique. Enseignement Math., 10, 267-270.
-
(1964)
Enseignement Math.
, vol.10
, pp. 267-270
-
-
Comtet, L.1
-
15
-
-
0003908675
-
-
Springer Verlag. An Introduction to Computational Algebraic Geometry and Commutative Algebra
-
Cox, D., Little, J., O'Shea, D. (1992). Ideals, Varieties, and Algorithms. Springer Verlag. An Introduction to Computational Algebraic Geometry and Commutative Algebra.
-
(1992)
Ideals, Varieties, and Algorithms
-
-
Cox, D.1
Little, J.2
O'Shea, D.3
-
16
-
-
0010153526
-
A short WZ-style proof of Abel's identity
-
The Foata Festschrift
-
Ekhad, S. B., Majewicz, J. E. (1996). A short WZ-style proof of Abel's identity. Electronic J. Combin., 3 (2). The Foata Festschrift.
-
(1996)
Electronic J. Combin.
, vol.3
, Issue.2
-
-
Ekhad, S.B.1
Majewicz, J.E.2
-
17
-
-
0003864328
-
-
R. E. Krieger publishing Company, Inc.
-
Erdélyi, A. (1981). Higher Transcendental Functions, volume 1-2-3. R. E. Krieger publishing Company, Inc.
-
(1981)
Higher Transcendental Functions
, vol.1-3
-
-
Erdélyi, A.1
-
19
-
-
0000873368
-
Some generalized hypergeometric polynomials
-
Fasenmyer, M. C. (1947). Some generalized hypergeometric polynomials. Bull. Am. Math. Soc., 53, 806-812.
-
(1947)
Bull. Am. Math. Soc.
, vol.53
, pp. 806-812
-
-
Fasenmyer, M.C.1
-
20
-
-
0003017043
-
A note on pure recurrence relations
-
Fasenmyer, M. C. (1949). A note on pure recurrence relations. Am. Math. Monthly, 56, 14-17.
-
(1949)
Am. Math. Monthly
, vol.56
, pp. 14-17
-
-
Fasenmyer, M.C.1
-
21
-
-
25944479355
-
Efficient computation of zero-dimensional gröbner bases by change of ordering
-
Faugère, J.-C., Gianni, P., Lazard, D., Mora, T. (1993). Efficient computation of zero-dimensional Gröbner bases by change of ordering. J. Symb. Comput., 16, 329-344.
-
(1993)
J. Symb. Comput.
, vol.16
, pp. 329-344
-
-
Faugère, J.-C.1
Gianni, P.2
Lazard, D.3
Mora, T.4
-
22
-
-
85034434467
-
Some algorithmic questions on ideals of differential operators
-
Caviness, B. F., ed., Proceedings EUROCAL'85, Springer Verlag
-
Galligo, A. (1985). Some algorithmic questions on ideals of differential operators. In Caviness, B. F., ed., Proceedings EUROCAL'85, vol. 204 of Lecture Notes in Computer Science, pp. 413-421. Springer Verlag.
-
(1985)
Lecture Notes in Computer Science
, vol.204
, pp. 413-421
-
-
Galligo, A.1
-
24
-
-
85033813724
-
"One sugar cube, please" or selection strategies in the Buchberger algorithm
-
Watt, S. M., ed. ACM Press
-
Giovini, A., Mora, T., Niesi, G., Robbiano, L., Traverso, C. (1991). "One sugar cube, please" or selection strategies in the Buchberger algorithm. In Watt, S. M., ed., Symbolic and Algebraic Computation, pp. 49-54. ACM Press.
-
(1991)
Symbolic and Algebraic Computation
, pp. 49-54
-
-
Giovini, A.1
Mora, T.2
Niesi, G.3
Robbiano, L.4
Traverso, C.5
-
25
-
-
84984647753
-
Non-commutative Gröbner bases in algebras of solvable type
-
Kandri-Rody, A., Weispfenning, V. (1990). Non-commutative Gröbner bases in algebras of solvable type. J. Symb. Comput., 9, 1-26.
-
(1990)
J. Symb. Comput.
, vol.9
, pp. 1-26
-
-
Kandri-Rody, A.1
Weispfenning, V.2
-
26
-
-
0001135534
-
On the holonomic systems of linear differential equations II
-
Kashiwara, M. (1978). On the holonomic systems of linear differential equations II. Invent. Math., 49, 121-135.
-
(1978)
Invent. Math.
, vol.49
, pp. 121-135
-
-
Kashiwara, M.1
-
27
-
-
38248999979
-
On Zeilberger's algorithm and its q-analogue
-
Koornwinder, T. H. (1993). On Zeilberger's algorithm and its q-analogue. J. Comput. Appl. Math., 48, 91-111.
-
(1993)
J. Comput. Appl. Math.
, vol.48
, pp. 91-111
-
-
Koornwinder, T.H.1
-
28
-
-
0004226502
-
-
Reihe Mathematik. Verlag Shaker, Aachen, Germany. After the Ph. D. thesis, ISBN 3-86111-342-2
-
Kredel, H. (1993). Solvable Polynomial Rings. Reihe Mathematik. Verlag Shaker, Aachen, Germany. After the Ph. D. thesis, ISBN 3-86111-342-2.
-
(1993)
Solvable Polynomial Rings
-
-
Kredel, H.1
-
29
-
-
38249027261
-
The diagonal of a D-finite power series is D-finite
-
Lipshitz, L. (1988). The diagonal of a D-finite power series is D-finite. J. Algebra, 113, 373-378.
-
(1988)
J. Algebra
, vol.113
, pp. 373-378
-
-
Lipshitz, L.1
-
30
-
-
0000472034
-
D-finite power series
-
Lipshitz, L. (1989). D-finite power series. J. Algebra, 122, 353-373.
-
(1989)
J. Algebra
, vol.122
, pp. 353-373
-
-
Lipshitz, L.1
-
31
-
-
0028767836
-
An introduction to commutative and noncommutative Gröbner bases
-
Mora, T. (1994). An introduction to commutative and noncommutative Gröbner bases. Theor. Comput. Sci., 134, 131-173.
-
(1994)
Theor. Comput. Sci.
, vol.134
, pp. 131-173
-
-
Mora, T.1
-
32
-
-
0001072553
-
Theory of non-commutative polynomials
-
Ore, O. (1933). Theory of non-commutative polynomials. Ann. Math., 34, 480-508.
-
(1933)
Ann. Math.
, vol.34
, pp. 480-508
-
-
Ore, O.1
-
33
-
-
38249008363
-
A WZ-style proof of Jacobi polynomials' generating function
-
Parnes, S., Ekhad, S. B. (1992). A WZ-style proof of Jacobi polynomials' generating function. Discrete Math., 110, 263-264.
-
(1992)
Discrete Math.
, vol.110
, pp. 263-264
-
-
Parnes, S.1
Ekhad, S.B.2
-
34
-
-
0002813555
-
Short and easy computer proofs of the Rogers-Ramanujan identities and of identities of similar type
-
Paule, P. (1994). Short and easy computer proofs of the Rogers-Ramanujan identities and of identities of similar type. Electronic J. Combin., 1 (R10), 1-9.
-
(1994)
Electronic J. Combin.
, vol.1
, Issue.R10
, pp. 1-9
-
-
Paule, P.1
-
35
-
-
0001487910
-
A mathematica q-analogue of Zeilberger's algorithm based on an algebraically motivated approach to q-hypergeometric telescoping
-
Toronto, Ontario. American Mathematical Society
-
Paule, P., Riese, A. (1997). A Mathematica q-analogue of Zeilberger's algorithm based on an algebraically motivated approach to q-hypergeometric telescoping. In Fields Proceedings of the Workshop "Special Functions, q-Series and Related Topics", 12-23 June 1995, Toronto, Ontario. American Mathematical Society.
-
(1997)
Fields Proceedings of the Workshop "Special Functions, Q-series and Related Topics", 12-23 June 1995
-
-
Paule, P.1
Riese, A.2
-
36
-
-
0000210471
-
A mathematica version of Zeilberger's algorithm for proving binomial coefficient identities
-
Paule, P., Schorn, M. (1995). A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities. J. Symb. Comput., 20, 673-698.
-
(1995)
J. Symb. Comput.
, vol.20
, pp. 673-698
-
-
Paule, P.1
Schorn, M.2
-
37
-
-
85030052011
-
-
A=B. A. K. Peters, Ltd.
-
Petkovšek, M., Wilf, H., Zeilberger, D. (1996). A=B. A. K. Peters, Ltd.
-
(1996)
-
-
Petkovšek, M.1
Wilf, H.2
Zeilberger, D.3
-
38
-
-
0010153527
-
A generalization of Gosper's algorithm to bibasic hypergeometric summation
-
Riese, A. (1996). A generalization of Gosper's algorithm to bibasic hypergeometric summation. Electronic J. Combin., 3(R19), 1-16.
-
(1996)
Electronic J. Combin.
, vol.3
, Issue.R19
, pp. 1-16
-
-
Riese, A.1
-
39
-
-
0010192627
-
Systèmes holonomes d'équations aux q-différences
-
Kashiwara, M., Monteiro-Fernandes, T., Schapira, P., eds, Berlin. Walter de Gruyter & Co. Proceedings of the Conference D-Modules and Microlocal Geometry, Lisbon, 1990
-
Sabbah, C. (1993). Systèmes holonomes d'équations aux q-différences. In Kashiwara, M., Monteiro-Fernandes, T., Schapira, P., eds, D-Modules and Microlocal Geometry, pp. 125-147, Berlin. Walter de Gruyter & Co. Proceedings of the Conference D-Modules and Microlocal Geometry, Lisbon, 1990.
-
(1993)
D-Modules and Microlocal Geometry
, pp. 125-147
-
-
Sabbah, C.1
-
40
-
-
0028443687
-
Gfun: A Maple package for the manipulation of generating and holonomic functions in one variable
-
Also available as Technical Report 143, INRIA
-
Salvy, B., Zimmermann, P. (1994). Gfun: a Maple package for the manipulation of generating and holonomic functions in one variable. ACM Trans. Math. Soft., 20, 163-177. Also available as Technical Report 143, INRIA.
-
(1994)
ACM Trans. Math. Soft.
, vol.20
, pp. 163-177
-
-
Salvy, B.1
Zimmermann, P.2
-
41
-
-
0000410641
-
Differentiably finite power series
-
Stanley, R. P. (1980). Differentiably finite power series. Eur. J. Combin., 1, 175-188.
-
(1980)
Eur. J. Combin.
, vol.1
, pp. 175-188
-
-
Stanley, R.P.1
-
42
-
-
0001579133
-
Binomial identities - Combinatorial and algorithmic aspects
-
Strehl, V. (1994). Binomial identities - combinatorial and algorithmic aspects. Discrete Math., 136, 309-346.
-
(1994)
Discrete Math.
, vol.136
, pp. 309-346
-
-
Strehl, V.1
-
43
-
-
0000089705
-
Gröbner basis and the problem of contiguous relations
-
Takayama, N. (1989). Gröbner basis and the problem of contiguous relations. Japan J. Appl. Math., 6, 147-160.
-
(1989)
Japan J. Appl. Math.
, vol.6
, pp. 147-160
-
-
Takayama, N.1
-
44
-
-
0025554847
-
An algorithm of constructing the integral of a module - An infinite dimensional analog of Gröbner basis
-
ACM and Addison-Wesley. Proceedings of ISSAC'90, Kyoto
-
Takayama, N. (1990a). An algorithm of constructing the integral of a module - an infinite dimensional analog of Gröbner basis. In Symbolic and Algebraic Computation, pp. 206-211. ACM and Addison-Wesley. Proceedings of ISSAC'90, Kyoto.
-
(1990)
Symbolic and Algebraic Computation
, pp. 206-211
-
-
Takayama, N.1
-
45
-
-
0025549971
-
Gröbner basis, integration and transcendental functions
-
ACM and Addison-Wesley. Proceedings ISSAC'90, Kyoto
-
Takayama, N. (1990b). Gröbner basis, integration and transcendental functions. In Symbolic and Algebraic Computation, pp. 152-156. ACM and Addison-Wesley. Proceedings ISSAC'90, Kyoto.
-
(1990)
Symbolic and Algebraic Computation
, pp. 152-156
-
-
Takayama, N.1
-
46
-
-
0000156626
-
An approach to the zero recognition problem by Buchberger algorithm
-
Takayama, N. (1992). An approach to the zero recognition problem by Buchberger algorithm. J. Symb. Comput., 14, 265-282.
-
(1992)
J. Symb. Comput.
, vol.14
, pp. 265-282
-
-
Takayama, N.1
-
47
-
-
85030051072
-
-
Private communication
-
Takayama, N. (1995). Private communication.
-
(1995)
-
-
Takayama, N.1
-
48
-
-
0010095231
-
Algorithm finding recurrence relations of binomial sums and its complexity
-
Takayama, N. (1996). Algorithm finding recurrence relations of binomial sums and its complexity. J. Symb. Comput., 20(5 and 6), 637-651.
-
(1996)
J. Symb. Comput.
, vol.20
, Issue.5-6
, pp. 637-651
-
-
Takayama, N.1
-
49
-
-
0002545645
-
Finite Gröbner bases in non-Noetherian skew polynomial rings
-
Wang, P. S., ed., New York. ACM Press. Proceedings ISSAC'92, July 1992, Berkeley, California
-
Weispfenning, V. (1992). Finite Gröbner bases in non-Noetherian skew polynomial rings. In Wang, P. S., ed., Symbolic and Algebraic Computation, pp. 329-334, New York. ACM Press. Proceedings ISSAC'92, July 1992, Berkeley, California.
-
(1992)
Symbolic and Algebraic Computation
, pp. 329-334
-
-
Weispfenning, V.1
-
50
-
-
0001169022
-
An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral identities
-
Wilf, H. S., Zeilberger, D. (1992a). An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral identities. Invent. Math., 108, 575-633.
-
(1992)
Invent. Math.
, vol.108
, pp. 575-633
-
-
Wilf, H.S.1
Zeilberger, D.2
-
51
-
-
84967728368
-
Rational function certification of multisum/integral/"q" identities
-
Wilf, H. S., Zeilberger, D. (1992b). Rational function certification of multisum/integral/"q" identities. Bull. Am. Math. Soc., 27, 148-153.
-
(1992)
Bull. Am. Math. Soc.
, vol.27
, pp. 148-153
-
-
Wilf, H.S.1
Zeilberger, D.2
-
52
-
-
0002128111
-
A fast algorithm for proving terminating hypergeometric identities
-
Zeilberger, D. (1990a). A fast algorithm for proving terminating hypergeometric identities. Discrete Math., 80, 207-211.
-
(1990)
Discrete Math.
, vol.80
, pp. 207-211
-
-
Zeilberger, D.1
-
53
-
-
0001601404
-
A holonomic systems approach to special functions identities
-
Zeilberger, D. (1990b). A holonomic systems approach to special functions identities. J. Comput. Appl. Math., 32, 321-368.
-
(1990)
J. Comput. Appl. Math.
, vol.32
, pp. 321-368
-
-
Zeilberger, D.1
-
54
-
-
0010196590
-
A Maple program for proving hypergeometric identities
-
Zeilberger, D. (1991a). A Maple program for proving hypergeometric identities. SIGSAM Bull., 25, 4-13.
-
(1991)
SIGSAM Bull.
, vol.25
, pp. 4-13
-
-
Zeilberger, D.1
-
55
-
-
73949145301
-
The method of creative telescoping
-
Zeilberger, D. (1991b). The method of creative telescoping. J. Symb. Comput., 11, 195-204.
-
(1991)
J. Symb. Comput.
, vol.11
, pp. 195-204
-
-
Zeilberger, D.1
|