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Egorychev G.P. — Integral Representation and the Computation of Combinatorial Sums
Egorychev G.P. — Integral Representation and the Computation of Combinatorial Sums

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Название: Integral Representation and the Computation of Combinatorial Sums

Автор: Egorychev G.P.

Аннотация:

This monograph should be of interest to a broad spectrum of readers: specialists in discrete and continuous mathematics, physicists, engineers, and others interested in computing sums and applying complex analysis in discrete mathematics. It contains investigations on the problem of finding integral representations for and computing finite and infinite sums (generating functions); these arise in practice in combinatorial analysis, the theory of algorithms and programming on a computer, probability theory, group theory, and function theory, as well as in physics and other areas of knowledge. A general approach is presented for computing sums and other expressions in closed form by reducing them to one-dimensional and multiple integrals, most often to contour integrals.


Язык: en

Рубрика: Математика/Алгебра/Комбинаторика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1984

Количество страниц: 286

Добавлена в каталог: 19.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $F_n^q$      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, $\phantom{}_n\Psi_n$      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, $\phantom{}_n H_n$      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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