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Nevanlinna R., Paatero V. — Introduction to Complex Analysis
Nevanlinna R., Paatero V. — Introduction to Complex Analysis

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Название: Introduction to Complex Analysis

Авторы: Nevanlinna R., Paatero V.

Язык: en

Рубрика: Математика/Анализ/Комплексный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1969

Количество страниц: 348

Добавлена в каталог: 21.10.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Gamma$-function      171
$\Gamma$-function and factorial      279
$\Gamma$-function, analytic continuation      280
$\Gamma$-function, product representation      285
Abel power series theorem      100
Abel, N.      100
Abelian group      29
Abelian integral      277
Absolute convergence      97 227 251
Absolute value      6
Accessible boundary point      318
Accumulation point      9
Addition theorem for $\varphi$-function      264
Addition theorem for doubly periodic function      264
Addition theorem for exponential function      66
Addition theorem for sine and cosine      79
Algebraic singularity      216
Analytic continuation      213—224
Analytic continuation of $\Gamma$-function      280
Analytic continuation, direct      214
Analytic function      1
Analytic function defined by integral      136
Analytic function singularities      149—155
Analytic function, complete      215
Analytic function, uniqueness theorem      139
Angle between two rays      16
Angle between two vectors      2
Angular defect      57
Arbitrary rectifiable curve      120
ARC      108
Arc cos z      87 91
Arc cot z      86
Arc length      50 111
Arc sin z      87
Arc tan z      86
Argument      6 11 74
Argument principle      175—181 314
Asymptotic value      66
Automorphic function      271 336
Axioms for plane Euclidean geometry      2
Axioms for two-dimensional vector space      1
Axioms, field      3
Basis of a group      126
Basis of vector plane      2
Bernoulli numbers      182 293
Bieberbach area theorem      183
Bilinear form      3
Bilinear transformation      37
Binomial equation      23
Binomial series      136
Blaschke product      239
Bolyai      50
Bolzano — Weierstrass theorem      20
Boundary correspondence of domain bounded by analytic curve      318
Boundary correspondence under conformal mapping      315
Boundary elements      318
Boundary point      10 313
Branch points      27 268
Branch points of the surface      163
Branches      25
c-points      33
Caratheodory, Constantin      143 309
Cartesian coordinate system      3
Cauchy consequences      138—146
Cauchy convergence criterion      96 110 157 207
Cauchy derivation for disk      131
Cauchy general form      133—135
Cauchy integral formula      131—135 168
Cauchy product rule      98 105 290
Cauchy theorem      117—127 167
Cauchy theorem, general form      125 208
Cauchy — Riemann conjugate harmonic functions      190
Cauchy — Riemann conjugate harmonic functions, polar form      22
Cauchy — Riemann conjugate harmonic functions, reflection principle      221
Cauchy — Riemann differential equations      12—14 29
Cauchy, Augustin      14
Chain rule      15 157
Circle of Apollonius      39
Circle of convergence      100
Circular arcs      51
Circular domain      45 47 49 145
Circular neighborhood      9 27
Circular triangle      58
Circular triangle, conformal mapping      166 334—335
Closed domain      10
Closed path      108
Closed plane      9
Closed set      9
Closure      10
Cluster point      9 317 338
Commutative group      29
Compact set      9
Complement      9
Complete analytic function      215
Complex conjugate      7 19 54
Complex line integral      108—114
Complex number notation      6
Complex plane      6
Composition of functions      15
Conditional convergence      97
Conformal function      16
Conformal mapping      37 73 305—342
Conformal mapping and Dirichlet problem      324
Conformal mapping and harmonic functions      190
Conformal mapping by analytic functions      15
Conformal mapping by schlicht function      162
Conformal mapping construction of solution      308—315
Conformal mapping of circular domains      45
Conformal mapping of Jordan domain      179 323
Conformal mapping of polygon      327 331
Conformal mapping of rectangle      334
Conformal mapping of triangle      331—334
Conformal mapping of unit disk      47 145 195
Conformal mapping, self-mapping      49
Conjugate groups      124
Conjugates, harmonic      15 190
Connectivity number      126
Continuation      see Analytic continuation
Continuity      10
Continuous deformation      123
Continuum      9
Contour lines      51
Convergence criterion      97
Convergence criterion and infinite products      225
Convergence, absolute      97 227
Convergence, circle of      102
Convergence, conditional      97
Convergence, radius of      102
Convergence, uniform      99
Convergent sequence      8
Convergent Series      95
Convex domain      120 216
Cosine      78
Cotangent      82
Covering surface      27
Cross-ratio      37
CYCLE      49 51
Cyclic group      28
Cyclic permutation      185 272
de La Vallee Poussin, C.      300
de Moivre's formula      7 67
Decomposition into partial fractions      33
Decomposition into real and imaginary parts      29
Definite integral      115
Deformation      122 128—130
Derivative      11
Derivative of exponential function      68
Differentiability      11
Differentiable function      11
Differential      11
Differential equation of $\varphi(z)$      261
DIMENSION      1
Direct analytic continuation      214
Dirichlet problem      204—206 211
Dirichlet problem and conformal mapping      324
Displacement vector      44
Domain      9
Domain, closed      10
Doubly periodic functions      243 334
Doubly periodic functions, addition theorem for      264
Doubly periodic functions, representation of      259 262
Element of an analytic function      214
Elementary deformation      122
Elliptic functions      243 246
Elliptic integral      262—275
Elliptic modular function      338
Elliptic transformation      43 48 51
Entire function      68 78 258 287
Equivalence relation      122
Equivalent      69
Equivalent boundary elements      319
Erdoes, P.      300
Essential singularity      150 216 245
Euler's $\Gamma$-function      278—304
Euler's constant      286
Euler's formulas      67 82 223
Euler's integral      278
Euler's product formula      289 295 301
Euler, Leonhard      135
Even functions      262
Exponential function      65—73 92 105
Exponential function, asymptotic values of      66
Exponential function, extension into complex domain      65
Exponential function, periodicity      68
Exponential function, reduction of simply periodic functions to      244
Extended plane      9
Exterior point      10
Fixed points      42
Fresnel integrals      181
Function element      214
Function, analytic      see Analytic function
Function, composition of      15
Function, conformal      16
Function, denned      10
Function, harmonic      14 184—191 320
Function, integral      68
Function, inverse      155—162 179 217
Function, monotone      323
Fundamental domain      72
Fundamental group      123
Fundamental period      244
Fundamental theorem of algebra      29 142 177
Fundamental theorem of differential calculus      186
Gauss mean-value theorem      135 140 195 209 236
Gauss, Carl Friedrich      135 300
General power      73
Geodesic      49
Goursat's proof      118 189
Goursat, Edouard      14
Graph      see Line-complex
Green's function      324 341
Group of integral values      125
Group, cyclic      28
Group, finite      28
Group, postulates      28
Hadamard's three-circle theorem      211
Hadamard, J.      300
Hardy, G.H.      299
Harmonic conjugates      15 190
Harmonic continuation      219
Harmonic functions      14 184—191 320
Harmonic measure      197 320
Harmonic sequence      41
Harnack's principle      206 240 312
Heine — Borel theorem      21 108
Hermite's method      292
Homeomorphic mapping      145
Homomorphism      124
Homothetic transformation      43
Homotopic      122
Homotopy      122 126 128
Homotopy classes      123
Hyperbolic geometry      48
Hyperbolic length      49
Hyperbolic measure      336
Hyperbolic transformation      43 48 50
Hypercycle      48 51
Image of a domain      160
Indirectly conformal      18
Infinite connectivity      126
Infinite products      225—228 286
Integrability condition      115 187
integral      108
Integral function      68
Integral theorem of Cauchy      131
Integration of a differential form      184
inversion      45
Involutory transformation      43
Isomorphism      124
Iteration method      309
Jensen's formula      236—239
Jordan arc      108 199 322 340
Jordan curve      108 177 200 314 323 340
Jordan domain      324 340
Jordan theorem      178
Kernel      196
Klein, Felix      337
Koebe, Paul      309
Landau, E.      299
Laplace differential equation      14 21
Laplace differential equation, polar form      22
Laplace integrals      171 173
Laurent derivation      146 151 236
Laurent expansion      146
Laurent series      167
Legendre modular function      271 337 342
Legendre modular function, normal form      274
Legendre relations      256
Legendre, A.M.      299
Leibniz      12
Length      2
Limit of a function      10
Limit of a sequence      8 138
Limit point      9
Lindelof theorems      199—204 322 340
Lindelof, Ernst      199
Line integral      108—113
Line integral, computation of      114
Line-complex      92 218
Linear transformation      4 37—45 144
Liouville's theorem      140 152 246 339
Littlewood, J.E.      300
Lobachevsky      50
Logarithm      71
Logarithmic pole      324
Logarithmic pole singularity      216
Loxodromic transformation      44
Majorant series      99 253
Mapping by elliptic integral      274
Mapping by power function      24
Mapping of doubly periodic function      268—272
Mapping, elliptic      43 48 51
Mapping, homeomorphic      145
Mapping, homothetic      43
Mapping, hyperbolic      48 52
Mapping, parabolic      44 48
Maximum principle      141 237 321
Maximum-minimum principles      192—195 199 220 325
Measure, harmonic      197 320
Measure, hyperbolic      336
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