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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 |
Powers, with matrix exponent 133
Prime end 385
Principal part 212 655 656 657 662
Principal part at infinity 216
Principal part of Laurent series 555
Principal part of meromorphic function 596
Principal part of rational function 217 574 583
Principal value integral 260 262 265
Principal value of argument 294
Principal value of logarithm 294
Principle of boundary map 401 424
Principle of maximum 86 104 332 355 541
Product of elements of group 1 10 45
Product rule of differentiation 19 53
Profiles, cascade of 367
Projection, stereographic 308
Proximity test 501 514—519
Proximity test with linear convergence function 506—508 510 512 522
Proximity test, equivalent 503
Proximity test, sharp 508
Proximity test, similar 503
Quadratic factor, multiple 561
Quadratic factor, of denominator of rational function 559
Quotient field 51
Quotient-difference algorithm 17 500 588 591 613 640 641 663
Quotient-difference algorithm, extended 662
Quotient-difference algorithm, progressive form of 614 619
Quotient-difference scheme 649
Quotient-difference scheme of rational function 650 653
Quotient-difference scheme, associated with formal power series 610
Quotient-difference scheme, construction by diagonals 619 620
Quotient-difference scheme, existence of 610
Quotient-difference scheme, extended 615
Range of arc 165
Range of function 72
Rational function 252 253 256 264 267 553—584 603 613 626 638 639 653
Rational function, integration of 562
Real part 7
Rearrangement of power series 140 142 144 151 152 170 171
Reciprocal of formal Laurent series 53
Reciprocal of formal power series 12 13
Rectangle, mapping of 416
Reduction factor 174
Reflection principle 389 390 391 398 399
Region 145
Region, circular 405 406 464 465—468 472 474 475 477 480 535 537 538
Region, convex 168
Region, homeomorphic 169
Region, simply connected 168 170 199
Region, starlike 285
Remainder in polynomial division 446
Representation of function by power series 87
Residue at isolated singularity 242 243 244 253 256 257 259 261 267 270 661
Residue of formal Laurent series 53 54—59 61 63 101 104 119 370
Residue of formal Laurent series, calculation of 55 57 118
Residue of rational function 630—632
Residue, determination of 243—245 559 577 630—632
Resolvent of eigenvalue problem 607
Reversion of almost unit 47 48 49 55—61
Rhombus rules 609 616 617
Riemann integral 181 184
Riemann mapping theorem 380 525
Riemann number sphere 308
Riemann number sphere, north pole of 307
Riemann number sphere, rigid motions of 312
Riemann sum 181 182 188 189 190 193 659
Riemann zeta function 279
Riemann's theorem, on isolated singularities 148 213
Riemannian theory, of analytic functions 143
Rotation 288 303
Rouche's theorem 280 284 494 495 524 535
Rounding errors 613 651
Rounding factor 429
Rule of composition 1
Rutishauser's rule 642 645 651 652 653
Saalschuetz formula 33 34 42
Saint — Venant's theorem 375
Schur transform of polynomial 493 496 497
Schur — Cohn algorithm 494 508 520 535
Schur — Cohn algorithm, implementation of 552
Schur — Cohn test 508 509 510 519
Schur — Jabotinski theorem 55
Schwarz — Christoffel map 396—416
Schwarz — Christoffel map, rounding corners in 422—431
Schwarz, lemma of 379 386 387 525 526
Search, methods of 499 513
Section of matrix 14
Semigroup 2 3 12 13
Sequence, geometric 509
Sequence, geometric, of analytic functions 159
Sequence, geometric, of entire functions 284
Series see also “Fourier series” “Laurent “Power
Series of Bessel functions 164 165 227 229
Series of rational functions 267 564 569
Series, uniform convergence of 75
Set, bounded 160
| Set, closed 160
Set, compact 160
Set, convex 168
Set, open 139 144
Set, open, connected 145
Sign change 439 487 489
Similarity 288
Sine function 110 266 660 661
Singular part see “Principal part”
Singularity, essential 215
Singularity, isolated 148 212 656 657
Singularity, isolated, at infinity 215
Singularity, removable 148 213 379
Skew field 8
Slit, region with 385
Sources and sinks, of flow 356
Space, complete 69
Space, linear 67
Space, metric 310
Space, normed linear 68
Square root, under composition 50
Square, pregnant 516
Square, suspect 517
Stability 279
Stability of polynomial 551
Stability, abscissa of 490 491
Stability, numerical 499 662
Stagnation point 359
Star, mapping exterior of 395 415
Stieltjes integral 605
Stirling's formula 176 222
Stodola's condition, for stability of polynomial 488
Stokes, theorem of 330 360
streamline 340 359
Stretching 288
Sturm sequence 444 516
Subdivision 187 638
Subdivision, norm of 187
Summation by Lagrange — Burmann formula 59—61 119
Summation of Fourier series 270
Summation of series of rational functions 267 264—569
Symmetry principle 320 392 396;
Symmetry with respect to circle 317
Symmetry with respect to generalized circle 318 31
Tangens function 110 111 112 266
Tangent vector 166 328
Taylor expansion 142 248 547 548 577
Taylor expansion of Hadamard polynomials 634
Taylor expansion of meromorphic function 612
Taylor expansion of rational function 569 586 605 613 638 639 662
Taylor's formula 545
Taylor's theorem 142 268 528
Thunderstorm 352
Torsional rigidity 372 377
Transfer function 279
Transformation, bilinear 300
Transformation, fractional linear 300
Transformation, quadratic, of hypergeometric series 42 43 229 421
Translation 303
Transplant of harmonic function 337
Transplantation, conformal 334 335 343 372
Transposition 591
Triangle inequality for complex numbers 7
Triangle inequality for vectors 68
Turbulence 422
Undetermined coefficients, method of 553 562
Unit disk, punctured 145
Unit, of integral domain 12 91
Van Vleck's theorem, on polynomial zeros 459
Vandermonde's theorem 24 28 29 48 92 172 176 461
Variables, separation of 342
Velocity, complex 364
Vieta's formulas 453 493
Watson's formula 62
Weierstrass double series theorem 133 161 184 186 222 661
Weierstrass M-test 75
Weight function 630
Weyl's algorithm 517 522 550 551
Whipple's formula 43
Winding number 233 277 383 485 515 516 517 520
Winding number, numerical determination of 234 239
work function 506 509
Wronski formula 17 616
Zeros of analytic function 89
Zeros of entire function by qd algorithm 619
Zeros of higher multiplicity of polynomial 438
Zeros of meromorphic function by qd algorithm 617
Zeros, clusters of 514
Zeros, clusters of, in half-plane 485
Zeros, clusters of, in interval 448
Zeros, location of 514
Zeros, multiplicity of 89 514
Zeros, number of, in disk 491
Zeros, order of 89
Zeros, refining of 484
Zeros, simultaneous determination of 537
Zeros, specified number of 450
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