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Henrici P. — Applied and Computational Complex Analysis. I: Power Series, Integration, Conformal Mapping, Location of Zeros.
Henrici P. — Applied and Computational Complex Analysis. I: Power Series, Integration, Conformal Mapping, Location of Zeros.



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Название: Applied and Computational Complex Analysis. I: Power Series, Integration, Conformal Mapping, Location of Zeros.

Автор: Henrici P.

Аннотация:

This volume, after laying the necessary foundations in the theory of power series and complex integration, discusses applications and basic theory (without the Riemann mapping theorem) of conformal mapping and the solution of algebraic and transcendental equations.


Язык: en

Рубрика: Математика/Анализ/Комплексный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 350

Добавлена в каталог: 06.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Function, analytic, scalar      89 139
Function, complex, of real variable      180
Function, complex-differentiable      325 328
Function, complex-valued      286
Function, continuous      73
Function, differentiable      143
Function, domain of definition of      72
Function, domain of values of      72
Function, doubly periodic      421
Function, elliptic      422
Function, even      93
Function, harmonic      332 336
Function, holomorphic      143 328
Function, homogeneous      646
Function, inverse      95
Function, inverse of exponential function      113 291 293
Function, inverse of Joukowski function      296
Function, inverse of Moebius transformation      302
Function, linear      288
Function, matrix-valued      122 138
Function, meromorphic      214 215 249 312 596 602 607 612 641 655
Function, odd      93
Function, one-to-one      95 291
Function, periodic      109 223 224 227 269 659
Function, quadratic      289
Function, range of      72
Function, rational      139 217 553 625 626
Function, scalar complex      139
Function, summatory      265
Function, trivial      95
Function, univalent      291
Function, value of      72
Functions, analytic, sequence of      see “Weierstrass double series theorem”
Fundamental theorem of algebra      105 159 378
Fundamental theorem of algebra, proofs of      138 280 552
Galois, theorem of      497
Gamma function      153 186 412 655
Gauss-Lucas theorem      463 465 474 518
Gaussian elimination      554 627
Gegenbauer polynomials      43 121 137
Generating function      60 61 138 578—585 587 590
Generating function of Bernoulli numbers      13 111
Generating function of Bessel functions      221
Generating function of Jacobi polynomials      119
Generating function of Laguerre polynomials      119
Generating function of Legendre polynomials      60 247
Geometric series      207 210 225 460 580 597
Gershgorin bounds      663
Gershgorin disk theorem      636 639 640
Goursat's theorem      285 330
Grace, theorem of      472 473 474
Gradient, complex      334 346 349 544
Graeffe's method      500 552
Graph of real function      286
Grid, rectangular or hexagonal      503 505
Group      1 2 8 45
Group of Moebius transformations      302 307
Group, abelian      2 608
Group, non-abelian      8
Hadamard polynomials      625 626 627 630 633 634 642 663
Hadamard product      13 576
Hadamard, theorem of, on product of power series      576
Half-plane right      145
Hankel determinants      574 591 594 596 600 615 616 662 663
Hankel determinants, associated with rational function      603
Hankel determinants, asymptotic behavior of      602 612 646
Hankel determinants, recursive computation of      596
Hankel polynomials      622 625
Heine — Borel lemma      160 161 168
Helmholtz equation      342
Hermite polynomials      37 43
Hodograph plane      369
Homeomorphism      382
Homotopy      167 179
Horner algorithm      435 437 508 513 551 561 567 569
Horner scheme      437 438 556
Hurwitz, theorem of      283 284
Hyperbola      295 343
Hyperbola, mapping of interior of branch of      395
Hypergeometric series, classical      27 34 39 40 42 44 48 62 118 150 226 229 417 421
Hypergeometric series, confluent      27 29
Hypergeometric series, confluent, zeros of      662
Hypergeometric series, generalized      27 32—34 37 39 40 43 44 47 62 65 220 221
Hypergeometric series, generalized, differential equation satisfied by      29
Hypergeometric series, generalized, radius of convergence of      80
Hypothesis (H)      642 649
Identity element      1 8 11 45 303
Identity principle for analytic functions      88 147
Imaginary part      7
Imaginary unit      4
Inclusion disk      484 540
Inclusion radius      457 473 500
Inclusion radius, proper      457
Inclusion region, for poles of rational function      640
Inclusion set      514
Index critical      642 645 646 647 650 653
Influence      352
Instability, numerical      613
Integral of trigonometric functions      183
Integral of trigonometric functions, improper      254 255 262—264
Integral with respect to arc length      193
Integral with respect to parameter      183 184—186
Integral, along arc      188 189—194
Integral, along closed curve      195 200—206 233 243 245 246 247 249 252 257 265 272 277 350 351 353 366 628
Integral, domain      2 11 12 51 89
Integral, elliptic      417
Integral, improper      251
Integral, improper, of rational functions      253—254 263 264
Integral, improper, with fractional powers      257 264
Integral, improper, with logarithms      257 264
Integration of ordinary differential equations      662
Integration, numerical      234 517 590 621
Interior of Jordan curve      235 243 245—249 252 278 280 282 382 383
Interpolation by polynomials      572
Interpolation by polynomials, Lagrangian formula for      601
Interpolation by sums of exponentials      571 577 622 662
Interpolation by sums of exponentials, algorithmic solution of      631—632
Inverse in Banach algebra      72
Inverse of element in group      1 4 8 12 46
Inverse of Moebius transformation      303
Inversion $z{\to}z^{-1}$      303 381 591
Involution      306
Isomorphism      15 46 302
Iterates of Moebius transformation      306
Iteration      523—552
Iteration function      533 542
Iteration function of arbitrary order      529
Iteration function of order three      531
Iteration function, Laguerre's      500 532 534
Iteration function, Newton's      529 531 532
Iteration function, order of      526
Iteration sequence      523 527 546
J.C.P. Miller formula      42 43 64 65 579
J.C.P. Miller formula, extension of      55
Jacobi polynomial      119
Jacobi's identity for Hankel determinants      595 611
Jacobi's identity for Hankel polynomials      622
Jacobi's transformation      63 65 228
Jacobian matrix of conformal map      339
Jordan block      128 130
Jordan canonical form      127 130 305 306
Jordan curve      235 243 245 246 266 269 272 278 279 282 330 331 366 383 485 515 520 628
Jordan curve theorem      235 285
Jordan curve, positively oriented      235
Jordan region      382 383 384 391
Jordan's lemma      255 256
Joukowski flow      367
Joukowski hypothesis      365 370
Joukowski map      294 299 315 345 353 359 367 394 395 415
Kahan's theorem      534
Kakeya-Enestroem theorem      284 462 497
Kapteyn series      165
Kepler's equation      119 120 130 226 230
Kummer's first identity      29
L-R algorithm      641
Lagrange — Burmann expansion      58 65 97 100 101 104 138 226 249 370 529
Lagrange — Burmann expansion, convergent      100 102 104 119 120 138
Laguerre polynomial      119 618
Laguerre polynomial, generating function of      119
Laguerre's theorem on polynomial zeros      466 473 480
Laguerre's theorem, generalization of      478 534
Laplace's expansion      592 593 607
Laurent series      209 224 226 369 370 381 559
Laurent series, formal      51 52 54—56 59 627 628 630
Laurent series, multiplication of      219
Laurent series, uniqueness of      209 219
Laurent's theorem      209
Legendre function      226
Legendre polynomial      42 60 164 284
Legendre polynomial, generating function of      60 247
Lehmer covering      512
Lehmer's method      492
Leibniz rule for differentiation of product      144
Lemniscate      299
Length of rectifiable curve      188
Limes inferior      76
Limes superior      76
Limit, of function      73
Liouville's theorem      159 218 400 525 659
Logarithm      112 147 179 203 232 233 257 294
Logarithm of matrix      131 138
Logarithm, analytic branch of      203
Logarithm, principal value of      114
Logarithm, simple branch of      114
Logarithmic series      49 50 115
MAP      377
Map, conformal      329
Map, topological      382
Mapping of interior of ellipse      394
Mapping of interior of parabola      392
Mapping of regular n-gon      411
Mapping of triangle      407
Mapping of two-gon      406
Mapping theorem for disks      321
Mapping theorem for simply connected regions      378
Matrix, diagonal      306 630
Matrix, equivalent      299
Matrix, exponential      122
Matrix, non-singular      16 72 303
Matrix, partitioned      653
Matrix, semi-circulant      14
Matrix, similar      123
Matrix, triangular      171
Matrix, tridiagonal      635 653
Matrix, unitary      313 314
Matrix, upper triangular      14 45 47 314
Maximum for scalar analytic functions      104
Maximum, principle of      86 332 355 379 541
Method of descent      541
Metric, chordal      311
Mittag — Leffler theorem      655
Model problem      344 346 352 357 358 364 368 407 409
Modulus      5
Modulus of doubly connected region      386 391
Moebius transformation      300 348 376 384 389 418 419 463 465 474 491 524 662
Moebius transformation, composition of Schwarz — Christoffel map with      404
Moebius transformation, entire      316
Moebius transformation, group of      302
Moebius transformation, standard representation of      304 314
Moivre's formula      9
Moment of inertia polar      341
Monodromy theorem      167
Monodromy theorem for simply connected regions      168
Montel's theorem, on polynomial zeros      459
Neighborhood      73
Neumann series (of Bessel functions)      164
Newton correction      454 467 468 477 478 544
Newton's formula      479
Newton's method      121 528 532 533 547 651
Newton's method for polynomials      534—541
Newton's method with wrong sign      534
Nilpotent      79
Non-unit, in integral domain of formal power series      12 35 38 40 41 43 45 51
Norm      68 173
Norm, column sum      71
Norm, Euclidean      68
Norm, induced      71
Norm, of vector      173
Norm, row sum      71
Norm, spectral      71
Normality of formal power series      605
Null function      464
Nyquist diagram      279 280
Obstacle      380
Orthogonality of Hadamard polynomials      628
Osgood — Caratheodory theorem      383 384 397
Pade table      663
parabola      290 392
Partial fraction decomposition      218 565 631 662
Partial fraction decomposition of rational function      553 557
Partial fraction decomposition real      556
Partial fraction expansion      658
Partial fraction expansion of cotagens function      660
Partial fraction expansion of meromorphic function      655
Partial fractions      159 553—661
Path      165
Period      109
Permutation      591 598 645
Picard's theorem      216
Pivotal points, system of      187
Plana summation formula      271 274 285
Plane, cut along negative real axis      145
Plane, model      337
Plane, physical      337
Pochhammer symbol      24 25—30 32—34 39 40 43 47 48 51 53 54 57 62 94 117 121 148 151 155—157 163—165 174 254 417 633
Point at infinity      300
Poisson equation      371
Polar representation, of curve      236
Pole      214
Pole, order of      214
Poles, of equal modulus      641
Polygon, mapping of exterior of      406 413
Polygon, mapping of interior of      396
Polygon, unbounded      401
Polynomial      10 85 105 139 159 198 264 281 283
Polynomial zeros, determination of      137 497—550 617—651
Polynomial, characteristic      635
Polynomial, convergence-generating      655 656
Polynomial, deflated      513
Polynomial, reciprocal      492
Polynomial, self-reciprocal      496
Polynomial, stable      488
Polynomial, Taylor coefficients of      437
Polynomial, Taylor expansion of      433
Polynomial, trigonometric      284
Polynomials, algebraic theory of      433
Polynomials, analytic theory of      551
Power function, general      115
Power function, principal value of      116
Power function, simple branch of      116 117
Power series, differentiation of      18
Power series, formal      9 576 578 585 604 609
Power series, hypernormal      606 607 615 617 620 621
Power series, normal      605 610 611 613 628—630 638 642
Power series, radius of convergence of      77 151 156 656
Power series, reciprocal of      12 615
Power series, reversion of      47 48 49 55—61
Power series, scalar      84
Power series, ultimately normal      605
Power sum      454 481
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