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Wilf H.S., Zeilbercer D., Petkovšek M. — A=B
Wilf H.S., Zeilbercer D., Petkov&#353ek M. — A=B

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Название: A=B

Авторы: Wilf H.S., Zeilbercer D., Petkovšek M.

Аннотация:

In the area of combinatorial identities computers are able to find very elegant proofs of difficult theorems unassisted by human intervention. This autonomy means that not only is it possible to use a PC to find such a proof, but also the proof can be checked easily. This book shows how several recently developed computer algorithms can master the difficult job of simplifying complex summations and if there is no such simplification they will prove this to be the case. The authors present the underlying mathematical theory of these methods, the principle theorems and proofs, and include a package of computer programs that can do these tasks.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 212

Добавлена в каталог: 14.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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