Dienes P. — The Taylor series: An introduction to the theory of functions of a complex variable :: Электронная библиотека попечительского совета мехмата МГУ

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Dienes P. — The Taylor series: An introduction to the theory of functions of a complex variable

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Название: The Taylor series: An introduction to the theory of functions of a complex variable

Автор: Dienes P.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1957

Количество страниц: 562

Добавлена в каталог: 28.03.2010

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

Предметный указатель

$K_{a}$ -matrix, $K_{a}$ -transformation      388
$\beta$ -matrix      397
$\gamma$ -matrix      397
'almost everywhere'      450
Abel sum      405
Abel transformation      405
Abel's scale      74
Abel's theorem      102 437
Absolute convergence      73
Absolute value      48
Absolutely convergent infinite product      92
Absolutely summable (B)      404
Algebraic function      327
Algebraic number      68
Analytic continuation      99
Analytic function      100
Analytic landscape      151
Appell's comparison theorem      101
Applies      384
Approached point      240
Argand's diagram (complex plane)      48
Argument of a complex number      109 118
Argument, principle of the      235
Arithmetic means      400 424—436
Associative algebra      60 61
B-summability      404
Base of an algebra      5 118
Bernoulli's inequality      41
Bernoulli's numbers      137 252
Bernoulli's polynomials      253
Biuniform mapping      164 266
Bolzano's theorem      13
Borel's integrals      302
Borel's lemma      26
Boundary point      27 179
Bounded derivates      450
Bounded set      2 13 22
Bounded variation      37
Bounds of a set      17
Bracketing of terms      93
Branch of a multiform function      128 219
Branch point      128
Cardinal number of a set      9
Cauchy product      85
Cauchy's conditions      143
Cauchy's fundamental formula      213 214
Cauchy's fundamental theorem      209 212
Cauchy's inequalities      147 223
Cauchy's n-th root test      75
Cauchy's test for a limit      52
cell      21
Central index      103
Central suffix      292
Characteristic numbers of a transformation      388
circle      21 109
Circle of convergence      75 76
Circle of meromorphy      321
Circular affinity      120
Circumference      179
Closed interval      12
Closed Jordan curve      177 208
Closed polygon      179
Closed set      19 22 179
Commutable matrices      412
Comparable, $\infty$       32
Comparison Test      71
Complete domain of uniform convergence      361
Complete residue      250
Complex number      47
Complex plane (Argand's diagram)      48 178
Condensation test      73
Conditional convergence      72 73
Conform-radius      165 274
Conformal representation      163
Conjugate complex numbers      48
Connected points of a set      27 179
Connectivity of domains      196
Connex set      27 28 179
Consistency      384 411
Continuous function      29 35
Continuum      192
Continuum ( $\equiv$ interval)      9
Convergent infinite product      91
Convergent sequence      16
Convergent Series      70
Converse theorems      471
Convex functions      155
Cross-cut      197
Curve      175—177 200
Curvilinear star domain      313
CYCLE      132
Cyclometric functions      116
Darboux's theorem      205
Decomposition of terms      93
Degree of infinity      498 499
Density direction      83
Derangement of series      80
Derivates of a function      450
Derived set      18
Diagonal      185
Diagonal matrix      409
Diameter of a set      24 51
Differential coefficient      142
Dini's theorem      104
Direct theorems      471
Discontinuity      29
Displacement of part of a series      82
Distance of points      24 178
Distance sets      23 24
Distinct diagonal matrix      414
Distinct sets      187
Distortion formula      279
Divergent infinite product      91
Divergent series      70
Domain      28 180
Dominant series      243 282
Doubly connected domain      196
Doubly infinite series      94
Ecart fini      490
Element of an analytic function      100
Elementary functions      8 110
Elliptic integral      249
Elliptic transformation      171
Enumerable set      9
Equality of real numbers      2 6
Equivalent algebras      59
Equivalent paths      265
Essential point      224 231
Euler's formula for the Gamma function      113
Euler's integers      170
Euler's integral of the first kind      141
Everywhere dense      22
Exponential function      76 106
Exponential mean      307 401
Exterior domain of a polygon      186
External point of an analytic function      240
Extreme limiting numbers      17
Extremum      149
Fatou's on regular points      467
Fatou's theorem on bounded functions      454
Final limit      94 95
Final limiting number      94
Finite increase      506
Finite span      490
Frobenius's theorem on complex algebras      62
Frobenius's theorem on series      102 437
Functional limit      30
Fundamental theorem of algebra      53 235
Gamma function      113
Gaps in the coefficients      231 361 381

Gauss's test      78
Generalized limit      384
Greatest limiting number      19
Hadamard gap      231 361 370
Hadamard's test for singular points      226 229 230
Hadamard's test function      230
Hadamard's theorem on the multiplication of singularities      346
Hadamard's three circles theorem      154
Hermite's polynomials      253
Hilbert matrix      410 414
Holomorphic function      90 222
Homologues      186
Hyper-elliptic integral      246
Hyperbolic functions      110 136
Hyperbolic transformation      171
Hypergeometric series      104
Implicit functions      245
Index of convergence      102 290
indices      7 106 118
Infinite product      91
Infinite series      70
Infinitely many      8
Infinity as a point      238
Inner conform radius      165 274
Inner neighbourhood      153
Inner point      16 26 179
Integrable functions      203
Integral of a uniform complex function      208
Interior domain of a polygon      186
interval      12
Inverse function      8
Inverse of a complex number      120 121
Inversion of a power series      137 246 260
Isolated number      12 22 50
Isomorphic algebras      59
Jensen's formula      237
Jordan curve      177 187
Jump of a function      29
Kojima matrix      388
Kronecker's theorem on rational functions      321
L'Hospital's rule, Stolz's extension of      403
Laurent's expansion      224
Least limiting number      19
Lebesgue integral      450
Left-hand upper and lower derivates      450
Length      178 200 202
LIMIT      15 50
Limit of a function (right-hand, left-hand)      31
Limiting number      12 14 50
Limiting point      22
Limiting values of a function      31
Limits of indetermination      32
Linear function      119 272
Linear magnification      163
Linear transformation      119 171
Liouville's theorem      148
Logarithm      7 118
Logarithm, Kiemann's surface of      128 129
Lower bound of a set      17
Lower integral      203
Lower rank of a sequence      409
Loxodromic transformation      171
Maclaurin's test      79
Mapping      120
Mapping function      165
Matrix      384
Maximum modulus      152
Maximum of a real function      149
Maximum type of integral functions      291
Maximum, principle of the      150 153
Meromorphic function      233
Minimum type of integral functions      291
Mittag-Leffler's mean      311
Modulus of a complex number      48
Monodromy, theorem of      264
Monotone function      38
Monotone sequence      2
Morera's theorem      221
Multiform function      8 117 123—125
Multiplication of singularities      346
N-th root test      75
Negative variation      39
Neighbourhood      17
Nevanlinna's formula      258
Nil-product      91
Nil-sequence      87
Non-continued Taylor series      227 872
Normal type of integral functions      291
Normed mapping function      165 274
O, o, notation for limits      33
Open interval      12
Open Jordan curve      177
Open set of points      27 179
Order of an integral function      291
Order of singularity      491
Oscillation of a real function      28
Outer conform radius      165 275
Outer point      27 179
Outside the range of a transformation      410
Overconvergence      356
Pade's table      481
Parabolic transformation      171
Parallel straight lines      178
Partial fractions      57
Partial integration      221
Path      202
Peano-curve      175
Perfect set      22
Picard's theorem on essential points      270 271
Picard's theorem on integral functions      270
Point      21 178
Point at infinity      238
Poisson's formula      215
Pole      224
Polygon      179
Polygon of summability      305
Polynomials      8
Positive variation      39
Power      5 118
Power of a set      9
Power series      146
Power series, division by      136
Power series, inversion of      137
Primary factor      288
Prime      56
Primitive roots of unity      382
Principal branch      117
Principal part      224
Principal star-domain      308
Principle of the argument      235
Principle of the maximum      150 153
Pringsheim's theorem      104
Quaternion algebra      60
Quaternion integer      68
Raabe's test      78
Radius of convergence      75 76 90
Range of a transformation      409
Ratio Test      76
Reached point      240
Real numbers      1
Real polynomials      57
Recti Sable curve      200
Reflexion in the unit circle      120 172
Region      27 179
Regular $\gamma$ -summation      418
Regular factor      488 489
Regular function      90 98 222 242
Regular point      230 241
Regular T-limit      418
Remainder of a series      72

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