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| Henrici P. — Applied and Computational Complex Analysis. I: Power Series, Integration, Conformal Mapping, Location of Zeros. |
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| Предметный указатель |
Abel's limit theorem 82 145 565
Abel's limit theorem, applications of 83
Absolute value 5
Accumulation, point of 73 88 146 147 152 655
Addition theorem for Bessel function 223 228
Addition theorem for exponential function 107 110
Addition theorem for exponential series 21 122
Algebra 70
Algebra complete normed 70; see “Banach algebra normed”
Algebraic complement 16 17 593
Algorithm see also “Quotient-difference algorithm”
Algorithm for computing poles of meromorphic function 608—651
Algorithm for computing winding number 239
Algorithm for evaluating derivatives of polynomial 433—437
Algorithm for partial fraction decomposition 553 557 562 656
Algorithm for starting Bernoulli's method 589
Algorithm for zeros of polynomials 497—551
Algorithm for zeros of polynomials, conditionally convergent 489
Algorithm for zeros of polynomials, convergent 498 549
Algorithm for zeros of polynomials, globally convergent 498
Algorithm for zeros of polynomials, locally convergent 498
Algorithm for zeros of polynomials, unconditionally convergent 498
Algorithm for zeros of polynomials, uniform convergence of 498 506 513 517 522 549
Almost unit 45 47 49
Amount of work in methods of search 505
Amount of work in Weyl's exclusion algorithm 521
Amount of work to construct Hadamard polynomials 634
Amount of work, for partial fraction decomposition 559 561
Anomaly eccentric 119
Anomaly mean 119
Apolar polynomial 472 473 474
ARC 165 187 230 231
arc, analytic 391
arc, differentiable 166
arc, geometrically equivalent 166 192
arc, homotopic 167
arc, initial point of 165
arc, opposite 192
arc, piecewise differentiable 166 190 191
arc, piecewise regular 166 191 232 233
arc, regular 166
arc, terminal point of 165
Area 339
Argument 5
Argument, continuous 230 485
Argument, increase of 231
Argument, principal value of 294 521 563
Argument, principle of 234 276 278 383 485 515
Arithmetic, circular 475 479 483 500 534 551
Arrangement, combinatorial 578—580
Associative law 2 3 11 45 46 303
Astroid 430
Asymptotic expansion 81
Bairstow's method 500 559
Banach algebra 71 72 77 81 87 89 90 90 92 93 95 99 101 103 133 143
Banach space 67 69 74 75
Basis of natural logarithms 107
Bernoulli numbers 13 64 111 112 269 661
Bernoulli polynomials 276
Bernoulli's law (in hydrodynamics) 365 368
Bernoulli's method 500 588 589 653 663
Bessel function 28 164 185 220 221 607 619
Bessel function, addition theorem for 223 228
Bessel function, asymptotic behavior of 228
Bessel function, complex zeros of 651 662
Bessel function, Poisson's integral for 228
Bessel function, zeros of 138 284
Bessel's integral 221 227
Binary representation 581
Binomial coefficient 21 461
Binomial coefficient, generalized 22
Binomial series 23 41 50 92 93 102 569
Binomial theorem 22 23
Birkhoff's theorem on polynomial zeros 456 512
Blasius, formula of 367
Boundary free 368
Boundary layer theory 425
Boundary of set 203 235
Boundary point accessible 385
Boundary point of set 235
Boundary, mapping of 382
Breakthrough electrostatic 422
Cable, capacity of condenser 350
Cable, excentric 346
Cable, per unit length 350
Cable, suspended 354
Cardano, formulas of 121
Cardoid 194
Casorati — Weierstrass theorem 215 216 218 378
Cauchy inclusion radius 58 459 462
Cauchy index 443
Cauchy index for interval 444 485 486 487
Cauchy integral formula 211 230 245 388 389 600 629
Cauchy integral formula for holomorphic functions 331 332
Cauchy kernel 207
Cauchy product 10 11 41 46 90 219 226
Cauchy sequence 69 134
Cauchy sequence, convergent 69
Cauchy — Hadamard formula 77 142 155 157 571 656
Cauchy — Riemann equations 326 328 336 544
Cauchy's estimate 84 86 90 91 96 98 134 156 159 211 332 530 597 657
Cauchy's integral theorem 232
Cauchy's integral theorem for disks 198
Cauchy's integral theorem for holomorphic functions 329 333
Cauchy's integral theorem for homotopic curves 200 207
Cauchy's integral theorem for simply connected regions 199 201 202 203 204
Cauchy's integral theorem, extended form of 204
Center of mass 341
Chain rule for formal power series 40 50 58
Channel with corner 412
Channel, flow through 357
Channel, suddenly narrowing 412
Channel, turnabout 413
Characteristic of field 8
Circle generalized 309 317 318 389
Circulation 361 370
Circulation, necessity of 365
Closed curve homotopic 199
Closure 73
Cluster of polynomial zeros 499 514
Coefficient of formal power series 10
Combinatorial analysis 578 662
Commutative law 2 8 11 50 70 303
Complex plane, extended 301
Component of open set 145 146 234
Component of set 637 638
Composition of analytic functions 95 116 404
Composition of formal power series 36 45 46 50 55 132
Composition of functions 94
Condenser 349
Condenser, cylindrical 351
Condenser, plate 344 355
Condenser, semi-infinite 409 426
Conductor 342
Confluence, method of 599 603 608 624
Conjugate of complex number 7
Continuation analytic 146 148
Continuation analytic by continuous continuation 387
Continuation analytic by functional relation relationships 152
Continuation analytic by patching 149
Continuation analytic by power series 149 150 170
Continuation analytic by rearranging power series 150 170
Continuation analytic by reflection 389
Continuation analytic by removing singularities 148
Continuation analytic, along arc 166
Continuation, fundamental lemma on 150
Continued fraction 490 614 663
Continuity, modulus of 190
Continuity, of zeros of polynomial 281
Control theory 487
| Convergence function 501 503
Convergence function of exclusion test 518
Convergence of series 75
Convergence, cubic 538
Convergence, function linear 506
Convergence, locally uniform 160 161 184
Convergence, order of 498
Convergence, quadratic 535 537
Convergence, speed of 526
Convergence, uniform 74 133 134
Convergence, uniform of power series 81
Convex hull, closed 464
Corner, concave 423 425
Corner, convex 429
Corner, re-entrant 423
Corner, rounding of 422
Cosine function 110
Cotangens function 110 111 137 660
Covering of set 160 503
Covering, optimal 512
Cross, mapping of 413
Crosscut 385
Curvature 186
Curve, closed 195 233
Curve, rectifiable 188
Curve, simple 235
Curve, starlike 205
Cycloid 186
Deflation 438
Derivative of analytic function 142
Derivative of complex function of real variable 180 181
Derivative of formal Laurent series 53
Derivative of formal power series 18 135 141 142
Derivative of function 129
Derivative of polynomial, with respect to point 466
Derivative, complex 327
Derivative, logarithmic 276 464 478
Descartes, rule of signs of 442
Descent function 542 546
Descent function, continuous 542 543 545
Descent function, Kellenberger's 548 549
Descent function, Nickel's 547
Descent function, Ward's 547
Descent, steepest 544 546 552
Determinant 16 17 496 591 592 663
Determinant of product of matrices 594
Determinant of sum of matrices 593 597
Determinant, Laplacian expansion of 592 593 601
Determinant, minor of 592
Determinant, minor of, algebraic complement of 593
Determinant, minor of, complement of 592
Determinant, Vandermondian 648
Diffeomorphism, piecewise 204 246
Difference equation 584 588 663
Difference equation of infinite order 589
Difference equation, basis of solution space of 586
Difference equation, solution of 585
Difference of polynomial 439
Difference operator 154
Difference scheme 608
Difference, divided 247 248
Differential 324 333
Differential equation, formal 20
Differentiation rules 181
Dirichlet integral 340
Dirichlet problem 337 342 343 350 373
Distance 310
Distance, chordal 311
Distance, Euclidean 523
Distributive law 2 3 11 46
Distributive law, right for composition 37 38
Divisor function 162
Divisor of zero 2 11
Dixon's formula 33 43 44
Domain of definition 72
Domain of values 72 286
Drawer problem 578—580
Eigenvalue of matrix 636 638—640
Eigenvalue, continuity of 636 663
Eigenvector 637
Electrostatics 342
Element regular 72
ellipse 194 206 263 295
Ellipse, circumference of 417
Emergency step 547
Enestroem's theorem 284 462 497
Epicycloid 194
Equation, analytic 101
Equation, biquadratic 121
Equation, cubic 118
Equation, Diophantine 582 584
Equation, trinomial 118 121
EQUIVALENCE 299
Estimate, a posteriori 498
Euclidean algorithm 487 489 490
Euclidean algorithm for rational functions 447
Euler's constant 275
Euler, first identity of 32 44
Euler, formulas of 110
Euler, result of (on representation of integers) 582
Euler, second identity of 40 150
Evolute 186
Exclusion algorithm 500
Exclusion test 517 518—522
Exclusion test, convergent 518
Exclusion test, one-sided 520
Exponential function 87 106 107 284 293
Exponential of matrix 122
Exponential series 20 50
Exponential, differential equation satisfied by 123
Extension, analytic 144 145—147
Factorial, generalized 24
Fast Fourier Transform 549 552
Fibonacci sequence 13 587 590
Field 3
Field of complex numbers 3
Field strength complex 346
Fixed point of analytic function 523—528
Fixed point of Moebius transformation 304 306
Flow, against dam 407
Flow, against rounded dam 424
Flow, around airfoil 365
Flow, around tilted blade 367
Flow, irrotational 356
Flow, past obstacle 358
Flow, potential 356
Flow, through cascade of airfoils 371
Flow, through circular grid 371
Flux 330 340
Force, complex 365
Force, complex, moment exerted by 369
Force, exerted on obstacle 365 367
Form factor 346
Fourier series 224 225 226 229 251 374 377 577
Fourier series with coefficients that are rational functions 269
Fourier series, absolutely convergent 71 72
Fourier series, considered as Laurent series 223 224
Fourier transforms of rational functions 254
Fourier-Budan, theorem of 443
Fresnel's integral 205
Function 72
Function, analytic 139
Function, analytic, abstract 138
Function, analytic, at infinity 216
Function, analytic, at point 87
Function, analytic, composition of 95
Function, analytic, defined by definite integral 183
Function, analytic, defined by limit process 161
Function, analytic, inversion of 97
Function, analytic, on set 144
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