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| C. Caratheodory, F. Steinhardt — Theory of Functions of a Complex Variable. 2 Volumes |
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Название: Theory of Functions of a Complex Variable. 2 Volumes
Авторы: C. Caratheodory, F. Steinhardt
Язык: 
Рубрика: Математика/
Статус предметного указателя: Готов указатель с номерами страниц
ed2k:
Издание: 2-d edition
Год издания: 1958
Количество страниц: 313
Добавлена в каталог: 11.11.2012
Операции: Положить на полку |
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| Предметный указатель |
Abel, N. H. 214
Abel’s transformation 214
Absolute convergence 198
Absolute value 9
Addition theorem, of exponential function 242
Addition theorem, of hyperbolic functions 249
Addition theorem, of tg z, tgh z 253
Addition theorem, of trigonometric functions 244
Algebraic branch point 264
Algebraic Riemann surface 264
Amplitude 13
Amplitude, principal 14
Analytic continuation 236
Analytic function 124 158
Angle-preserving 25
Argument 14
Artin, E. 289
Automorphism 8
Bernoulli numbers 273 ff.
Bernoulli numbers, polynomials 273 ff.
Bernoulli, Jakob 273 277
Bilinear transformation 21
Binet, J. 291
Binet’s function 291
Binomial series 264
Bohr — Mollerup theorem 288
Bohr, H. 288
Bolyai, J. 75
Boundary 91
Boundary value 95
Bouquet vii
Branch point 258 264
Briot vii
Bundle of circles 46
Calculus of finite differences 273
Cantor’s diagonal process 90
Caratheodory, C. 25 96
Catenary 250
Cauchy — Riemann equations 149
Cauchy, A. L. 18 94 125 127 227
Cauchy’s integral formula 127
Cauchy’s Theorem 125
Chordal distance 81
Chordal oscillation 175
Circle of convergence 203
Circle-preserving mapping 23
Circle-preserving mapping of the second kind 25
Clausen’s theorem 283
Closed point set 91
Closed point set, relative 96
Closure of a point set 91
Common points of a pencil 39
Compact family 183
Compact set 89
Completely separated curves 101
Complex conjugates 8
complex numbers 2
Complex plane 17
Complex plane, extended 26
Conformal mapping 41
Conjugate pencils 40
Connectivity 96
Continuous arc 97
Continuous convergence 173
Continuous function 93
Continuum 97
Contour integral 107
Convex function 289
Cross-cut of a region 105
Cross-ratio 29
Delambre, J. — B. — J. 61
Delambre’s formulas 61
Dense-in-itself 91
Derivative 119
Differentiable function 119
Distance invariants 52
Double-series theorem, Weierstrass 210
D’Alembert 7
Elliptic bundle 46
Elliptic metric 71
Elliptic pencil 40
Entire function 164
Equator of a bundle 47
Essential singularity 163
Euclid 75
Euler, L. vii 2 278
Eulerian triangles 60
Euler’s constant 284
Euler’s formulas 244
Exponential function 241
Extended complex plane 26
Exterior point 91
Family of functions 182
Family of functions, compact 183
Family of functions, normal 182 299 300
Fixed point 32
Frobenius 282
Frontier of a point set 91
Fundamental region 250
Fundamental theorem of algebra 8 167
Gamma function 286
Gauss, C. F., vii 2 7 17 61 75 167
Gaussian plane 17
Gauss’s product for gamma function 295
General power function 263
Geodesics 68
Goursat, P. 125
Group 22
Hamilton, W. R. 2
Harmonic function 150
Harmonic measure 154
Harmonic set 31
Harnack’s theorem 153
Herglotz, G. 269
Holder, O. 2 88
Horizon of the non — Euclidean plane 74
Hurwitz, A. 194
Hurwitz’ theorem 194
Hyperbolic bundle 46
Hyperbolic function 248
Hyperbolic pencil 38
Hypercycle 79
imaginary numbers 2
Imaginary part 7
Imaginary unit 6
Improper point 25
Infinity, point at 25
Integrable function 119
Integrable in the small 121
integral 119
Integral function 164
Integral linear transformation 26
Integral transcendental function 170
Integration by parts 231
Interior point 91
Inverse function 229
inversion 33
Involutory 8 34
Isogonal 25
Isolated point 91
Jacobi, C. G. J. vii
| Jordan arc 100
Jordan curve 100
Kepler’s equation 235
Kernel, normal 178
Klein, F. 60
Lacroix, P. vii
Lagrange, J. H. 235
Lagrange’s series 231
Laplacian operator 150
Laurent expansion 217
Laurent, M. P. H. 218
Legendre’s identity 297
Limit point 91
Limiting oscillation 175
Limiting point of a pencil 38
Limiting rotation 78
Limiting translation 78
Lindelof, E. viii
Linear transformation 21
Liouville’s theorem 165
Lobatchewsky, N. J. 75
Logarithm 256
Logarithmic branch point 258 259
Logarithmic residue 228
Loxodromic linear transformation 45
Lucas, E. 277
Machin, J. 254
Mapping, neighborhood-preserving 99
Mapping, topological 96
Maximum-modulus principle 133
Mean value 132
Mean-value theorem 114
Meromorphic function 159
Mittag — Leffler, G. 222
Mittag — Leffler’s theorem 222
Modulus 9
Moebius, A. F. 21
Moebius’ transformation 21
Mollerup, J. 289
Mollweide 61
Monodromy theorem 236
Montel, P. viii 183
Moore, E. H. 288
Morera’s theorem 130
Motions 50
Motions, non — Euclidean 76
Multiply connected region 102 ff. 104
Natural logarithm 256
Neighborhood 98
Neighborhood-preserving mapping 99
Normal family of functions 182
Normal kernel 178
Normal sequence of functions 178
Open kernel 91
Open set 91
Open set, relative 96
Oricycle 79
Osgood, W. F. 190
Osgood’s theorem 190
Ostrowski, A. viii 183 288
Parabolic bundle 46
Parabolic pencil 40
Partial fraction decomposition 161
Pencil of circle 38
Perfect point set 91
Periods, of exponential function 247
Periods, of trigonometric functions 250
Poincare, H. 79
Point, at infinity 25
Point, of accumulation 91
Poisson, S. D. 147
Poisson’s integral 146
Pole 159
Pole, simple 225
Polynomial 165
Potential function 150
Power series 201
Primitive period 248
Principal amplitude 14
Principal part 225
Principal value of logarithm 256
Principal value of power function 263
Pringsheim, A. vii 125
Pseudo-chordal distance 82
Ptolemy 27
Punctured plane 21
Pure imaginary numbers 10
Radius of convergence 203
Real analytic function 242
Real axis 17
Real numbers in the complex domain 5
Real part 7
Rectifiable curve 106
Reflections 32
Region 97
Regular analytic function 124
Residue 226
Residue, logarithmic 228
Riemann's theorem 130
Riemann, B. vii 18 27 130 259
Riemann’s inequality 157
Riemann’s sphere 27
Riemann’s surface 258 259
Rigid motions 50
Root of unity 15
Rotations of the sphere 210
Rouche, E. 228
Rouche’s Theorem 228
Schlicht function 196
Schmidt, E. 101
Schwarz, H. A. vii 146
Schwarz’s lemma 135
Simple closed curve 100
Simple function 196
Simple pole 225
Simply connected 103
Singularity 162
Spherical motion 56
Stereographic projection 27
Stieltjes, T. H. viii 236
Stirling’s series 291 296
Taylor series 205
Topological mapping 96
Transcendental function 170
Trigonometric functions 243
Ultra-parallel 74
Unconditional convergence 198
Uniform convergence 178 189
Uniformly bounded in the small 184
Uniformly continuous 95
Unimodular numbers 10
Vitali, G. 189
Vitali’s theorem 189
Von Staudt 283
Wallis, J. 271
Wallis’ formula 271
Weber, H. 60
Weierstrass, K. viii 222
Weierstrass’ double-series theorem 210
Weierstrass’ factorization theorem 222
Weierstrass’ theorem 163
Wellstein, J. 60
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