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Wilf H.S., Zeilbercer D., Petkovšek M. — A=B |
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Предметный указатель |
Abramov, Sergei A. 159 201
Adjoint operator 163
Algorithm, hypergeometric series lookup 36
Almkvist, Gert 180 201
Amer. Math. Monthly 27 88 104 193
Analytic continuation 42
Andrews, George 115 201
Angle bisectors 9
Archimedes 4
Askey, Richard 193 203
Asymptotic 133 134
Axiom 21
Bayer, David 202
Bell numbers 186
Bellman, Richard 202
Bender, Edward 202
Bergeron, Francis 193
Bessel function 34 38
Bi-basic equations 187
Binet's formula 12
Binomial coefficients 19 30 33
Binomial coefficients, sum of pth powers 72
Binomial coefficients, sum of the cubes of 20
Binomial coefficients, sum of the squares of 19
Bjoerk, J.E. 202
Bressoud, David 6 202
Bronstein, M. 201
Buchberger, Bruno 10 172 202
Canonical form 6 83
Cartier, P. 194 202
Cassini's formula 12
Catalan numbers 177
Cauchy — Schwarz inequality 9
Caviness, B.F. 202
Cayley 172
Certificate 24 28
Chimpanzee 26
Chou, Shang-Ching 202
Chu — Vandermonde identity 70 181 182
Cipra, Barry 202
Clausen's identity 43
Clinton, Bill 7
Closed form 6 19 20 30 33 60 114 141 157—159
Coefficient field 151
Cohn, R.M. 202
Companion identity 125 128—130 138—140
Comtet, Louis 203
Creative telescoping 142 143 164 165
d'Alembertian functions 144
d'Alembertian sequences 157 158
Daubechies, Ingrid 190 203
Davis, Martin 5
Davis, Philip J. 203
Degree bound 84 149 150
Derangements 158
Descartes, Rene 10
Diophantine equations 6
Discrete holonomic functions 184
Dixon's identity 136 183
Dixon, A.C. 203
Double factorial 89
Dougall's identity 43
Dual identity 127
EKHAD xi 11 59 104 112 139 176 194 195 197 198
Elimination 177
Elliptic functions 13
Euclid 4
Euclidean algorithm 8
Exponential function 20
Exponential generating function 186
Exponential series 35
FactorialSimplify 27 40 60
Factorization of operators 162
Falling factorial 66 149
Fasenmyer, Sister Mary Celine 18 23 30 55—59 61 64 105 106
Fasenmyer, Sister Mary Celine, algorithm of 58
Fermat's last theorem 13
fibonacci 5 12
Fibonacci numbers 166 172 174 176
Foata, Dominique 194 202
Fundamental theorem 64 68—70 105 106
Fundamental Theorem, r-variate 70
Gamma function 42 43
Gamma function, reflection formula 46
Gasper, George 204
Gauss, C.F. 23 42 126 130 133
Gaussian elimination 172
Generating function 22 24
Gessel, Ira 131 135
Giambruno, Antonio 91
Gillis, Joseph 194
Goedel, Kurt 4
Gosper, R.W., Jr., algorithm of 30 74 77
Gosper, R.W., Jr., degree bound in 84
Gosper-summable 74
Graham, Ronald L. 106 165 204
Grinch 22
Groebner bases 10 172 184
Group, additive 7
Hermite polynomials 195
Hilbert, David 4
Holonomic 175 180 186
Homo sapiens 24
Hornegger, J. 204
Howe, Roger 194
Hyper, algorithm 152—157 162 165—167
Hypergeometric database 30 33 42
Hypergeometric identities 22
Hypergeometric series 34
Hypergeometric series, lookup algorithm 36
Hypergeometric term 19 34 58 74 75
Hypergeometric term, proper 64
Hypergeometric term, similar 91
Identity 21
Identity of Reed — Dawson 63
Identity, binomial coefficient 22
Identity, hypergeometric 22
Identity, routinely verifiable 26
Identity, terminating 135
| Indefinite hypergeometric sums 30
Joyal, A. 193
k-free 65
Kac, Victor 193
Knopp, Marvin 204
Knuth, Donald E. ii ix 106 165 194
Koepf, W. 204
Koornwinder, T. 109 204
Krattenthaler, Christian 39 197
Kummer, E.E. 42
Labelle, Gilbert 193
Laguerre polynomials 61
Laurent polynomial 174
Lc (leading coefficient) 74
Leroux, Pierre 193
Linear algebra 171
Lisonek, P. 205
Logo, computer terminal 9
Loos, R. 205
Macaulay 10
MacDonald, I.G. 193
Macdonald, Ian 205
Macsyma 21
Majewicz, J.E. 192 203
Maple 21 29 41
Mathematica 21 27
Matiyasevich, Yuri 5
Mehler formula 194
Mills, W.H. 115 205
Morley's trisectors theorem 11
Multinomial coefficients 177
Myth 48
Normal form 6
Orszag, S.A. 202
P-recursive 175 185
Parnes, S. 203
Pascal's hexagon theorem 11
Patashnik, Oren 106 165 204
Paule, Peter 112 114 116 142 164 197 205
Petkovsek, Marko 18 31 103 114 115 117 121 165
Pfaff — Saalschuetz identity 195
Poly, algorithm 150 152
Polynomial identities 8
Polynomials 34
Polynomials, Chebyshev 34
Polynomials, Hermite 34
Polynomials, Laguerre 34 40
Proper hypergeometric term 64
Putnam Exam 153
Putnam, Hilary 5
qEKHAD 116 197 199
qHyper 156 200
Rahman, Mizan 204
Ratio Test 20
Recurrence 19
Recurrence with polynomial coefficients 20
Reflection formula 46
Regev, Amitai 91
Resultant 79
Ring of operators 145
Ring of sequences 144 146
Rising factorial 39 66 157
Robbins, D.P. 115 205
Robinson, Julia 5
Rogers — Ramanujan identity 117
Rota, G.C. 193
Routinely verifiable identity 26
rsolve 27 60
Rumsey, H. 115 205
Saalschuetz's identity 43
Schorn, Markus 112 114 142 197
Schuetzenberger, Marcel 194
Series, binomial 34
Series, exponential 34
Series, logarithmic 34
Series, nonterminating 39
Series, terminating 39
Series, trigonometric 34
Shadow 132
Similar hypergeometric functions 158 161 162
Similar hypergeometric term 91
Similarity 91
Simple formula 20
Stafford, J.T. 184 206
Stanley, Richard 175 206
Stembridge, John 13
Sticks and stones 171
Stillman, Mike 202
Stirling numbers 186
Strehl, Volker 195 205 206
Sums, definite 30 88 102 133 141
Sums, indefinite 30 87 102
Sums, multiple 6 19 71 185
Sylvester, J.J. 172
SymbolicSum 39
Symmetric function identities 12
Takayama, Nobuki 180 184 188
Theta functions 14
Transformation rule 49 136
Tre, Sol 203
Trees, rooted labeled 185
Undetermined coefficients 150
Universal Proof Machine 5
Vandermonde 70 130 133
Vandermonde — Chu identity 181
Verbaeten, P. 68
Viennot, X. 194
Wiles, Andrew 13
Wilf, Herbert S. 18 68 115 121 165
Wimp, J. 207
WorldWideWeb sites 11 197 206
WZ, method 24 25 30 143
WZ, pair 122 131 132 135 137 140
WZ, proof algorithm 27
WZ, standardized proof algorithm 25
Yen, Lily 69 207
Yesterday operator 173
Zeilberger, Doron 18 23 58 68 101—140
Zeilberger, Doron, algorithm of 30
Zeng, J. 195
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