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Egorychev G.P. — Integral Representation and the Computation of Combinatorial Sums |
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Предметный указатель |
Basis, homology 234
Boundary of a chain 233
Boundary of a simplex 233
Chain (singular) 233
Coefficient, linking, of cycles 239
CYCLE 234
Cycle, homologous to zero 234
Differential form 231
Differential form, closed 232
Differential form, exact 232
Differential form, holomorphic 233
Dual homology bases and cohomolgy bases in the de Rham sense 242
Dual homology bases in the Alexander — Pontryagin sense 239
Exterior differential of a form 231
Exterior multiplication 231
Formula of Kummer 71
Formula of Saalschiitz 71
Formula of Schwatt 41
Formula of Stokes 235
Formula, change of variables 235
Formula, integration by parts 237
Formula, Leray residue 244
Formula, Leray residue (multiple) 244
General position, manifolds in 244
General position, simplexes (chains) in 238
Generating function 12
Group, cohomology 232
Group, homology 234
Identity (identities) of Abel 49
Identity of Beineke and Pippert 185
Identity of Bizley 183
Identity of Carlitz 28 155 156 170 184 185
Identity of Cvetcovid and Simic 84
Identity of Davis 52
Identity of Dawson 151
Identity of Dawson, q-analogue of 77
Identity of Engelberg 79
Identity of Feller 84
Identity of Fjeldstad 182
Identity of Ftenyi 124 185
Identity of Goldberg 81
Identity of Gould 52 84 183
Identity of Govindarajulu and Suzuki 186
Identity of Grosswald 27
Identity of Gupta 48
Identity of Hagen 79 80
Identity of Hardy 25
Identity of Hietala and Winter 83
Identity of Jensen 50
Identity of Kaucky 72
Identity of Klee 78
Identity of Le-Jen Shoo 52 170
Identity of Lie 181 183
Identity of Lyamin and Selivanov 55
Identity of MacMahon 177
Identity of Marcia 84
Identity of Moriarty 52 74
Identity of Moriarty, q-analogue of 75
Identity of Nandjundiah 183
Identity of Nguyen-Huu-Bong 79
Identity of Riordan 183
Identity of Rodeja 50
Identity of Rohatgi 50
Identity of Rosembaum 83
Identity of Sarmanov, Sevast'yanov and Tarakanov 158
Identity of Sheehan 163
Identity of Shirokov and Signaevskit 57
Identity of Sitgreaves 83
Identity of Stechkin 54
Identity of Suranyi 183
Identity of Takacs 185
Identity of Tepper 47
Identity of Van Elbenhorst Tengerbergen 183
Identity of Wu 79
Identity with linear constraints on the summation indices 161 162 163
Index, intersection (of simplexes, chains) 238
Integral of a form over a chain 235
Kernal, Bergman 29 205
Kernal, Szego 188 192 203 205
| Manifold, complex analytic 230
Manifold, differentiate 230
Mapping of manifolds 232
Method of integral represenations of sums 9
Method of integral represenations of sums, computation algorithm 9
Method of integral represenations of sums, res (definition) 13
Method of integral represenations of sums, res (definition), rules for operation 13 15
Method splitting 168 172
Method, Gronwall summation 225
Number(s), Bernoulli (definition and integral representation) 272
Number(s), Bernoulli, generalized 274
Number(s), Betti 234
Number(s), binomial (and polynomial) coefficients 269 270
Number(s), combinatorial 119
Number(s), DeMorgan 91
Number(s), Euler 272 274
Number(s), Euler, generalized 274
Number(s), Stirling, generalized 273
Number(s), Stirling, of the first kind 272
Number(s), Stirling, of the second kind 273
Orientation of a manifold 230
Orientation of a simplex (chain, cycle) 233
Pair of inverse linear relations, definition 88
Pair, of Abel type 106
Pair, of exponential type 107
Pair, of Legendre type 105
Pair, of Legendre — Tchebycheff type 106
Pair, of ordinary type 107
Pair, of Tchebycheff type 104 105
Pair, of two-index type 108
Pair, of type 88
Pair, of type P(q, r, s) 109
Parameterization of a simplex (chain, cycle) 233 235
Partition function of Dyson 151
Polydisk (polycylinder) 18
Residue (multidimensional, multiple) 240 242
Residue class 244
Residue class, multiple 244
Series, 69
Series, Dirichlet 117 118
Series, hypergeometric, basic 69
Series, nearly-poised 69
Series, of Saalschuetz form 69
Series, of Saalschuetz form, generalized 69
Series, of Saalschuetz form, generalized, 69
Series, of Saalschuetz form, generalized, nearly-poised 69
Series, of Saalschuetz form, generalized, of Gauss 68
Series, of Saalschuetz form, generalized, of Saalschuetz form 69
Series, of Saalschuetz form, generalized, well-poised 69
Series, power, formal 12 115
Series, power, formal, of Euler type 118
Series, power, formal, of exponential type 117
Series, well-poised 69
Simplex (singular) 233
Singular set (surface) 229 237 239
Skeleton of a polycylinder (polydisk) 18
Sum, computation of, in closed form (definition) 60
Sum, multidimensional (multiple) 149
Theorem, Cauchy — Poincare 236
Theorem, Froissart decomposition 245
Theorem, generalized 252 253
Theorem, Hardy — Littlewood 138
Theorem, main 19
Theorem, main, generalization of 175
Theorem, master, of MacMahon 18 19
Theorem, of de Rham 241
Theorem, of Dougall 72
Theorem, of Freud 137
Theorem, of Leray 244
Theorem, of Lerch 70
Theorem, of Rouche (Rouche principle) 250
Theorem, of Saalschuetz 71
Theorem, of Szegoe 137
Theorem, on a generating function for a subsequence of a multiple sequence 170
Theorem, on residues 240 242
Theorem, on the multiple logarithmic residue 250 252
Zero of a system of holomorphic functions 249
Zero, multiple 250 252
Zero, simple 249
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