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Henrici P. — Applied and Computational Complex Analysis (Vol. 2)
Henrici P. — Applied and Computational Complex Analysis (Vol. 2)

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Название: Applied and Computational Complex Analysis (Vol. 2)

Автор: Henrici P.

Аннотация:

Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions.


Язык: en

Рубрика: Математика/Анализ/Комплексный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1977

Количество страниц: 662

Добавлена в каталог: 02.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$RITZ^{-1}$ fraction      525 526 529 550 560 561 597
$SITZ^{-1}$ fraction      see “S fraction”
$ST^{\ast}$      585 608
A stability      596
Abel, theorem of      48 161 325
Abelian theorem, on Laplace transforms      204 255 287 288 289 295
Abel’s integral equation      244
Actuarial mathematics      350
Adams’ formula      405
Admittance      235
Airy function      430
Airy’s integral      419 431
Algebra      362
Apollonius, circles of      504
Approximant      475 479 481 493 506 512 514 517 521 522 526 527 531 534 537 542 560 561 562 564 565 568 577 578 600 602 608 612 614 625
Approximant, represented by determinants      485
Approximants, consecutive      482 486
Approximations, successive      82 380 383 384
Arcsine      468
Arctangent      470 580 620
Arctangent, continued fraction for      534
Argument, continuous      106 107
Arithmetic, circular      503 507 509 511
Arithmetic, circular, rational      632
Ascending method, for evaluation of continued fraction      475 485
Asymptotic behavior      351
Asymptotics      351
Barrier      158
Bead      236
Beppo Levi, theorem of      30 31 41 304 358 365
Bernoulli function      220 455 456. 458
Bernoulli number      220 305 359. 377 397 442 454 458 470 624 626
Bernoulli polynomial      220 453 454 458
Bernoulli’s inequality      603 607
Bessel function      121 137 141 194 244 314 320 324
Bessel function of large order      422 425 427
Bessel function of second kind      138
Bessel function, algebraic nature of      140
Bessel function, asymptotic behavior of      72 252 255 275 349 394 395 405
Bessel function, modified      259 274 292 632 635 639
Bessel function, modified, asymptotic behavior of      405
Bessel function, Poisson’s integral for      142 244 273
Bessel function, quotient of      545
Bessel function, Sommerfeld’s integral for      344 347 349 350 422
Bessel function, zeros of      395 397
Bessel polynomials      560 641
Bessel’s equation      135 138 142 180 191 192 344 347 388 395
Bessel’s integral      431
beta function      55 56 58 618
Beta function, Euler’s integral for      55 405 435
Beta function, incomplete      62
Beta function, Pochhammer’s integral for      59
Binet function      39 42 46 357 362 365 368 377 456 457 624
Binomial series      45 421 447 535
Binomial theorem      48
Birnbaum’s inequality      640
Bode plot      231
Calculus, operational      197 212 234
Cantor’s diagonal process      564
Carleman’s condition      608 616 617 622 624 628 632
Carleman’s inequality      603 607
Carlson’s theorem      334
Cauchy criterion, for convergence      201 573
Cauchy criterion, for convergence, for convergence of double series      84
Cauchy — Hadamard formula      193 248 306 307 321 607 638
Cauchy’s estimate      88 92 445
Cauchy’s formula      376 414 444 448 460 563
Cauchy’s inequality      112
Cauchy’s test, for convergence      294
Cauchy’s Theorem      33 247 272 278 279 284 308 393
Celestial mechanics      113
Chain of poles      65 68
Chain of poles, ascending      63 64 65 66 71
Chain of poles, descending      63 65 66 69
Chess match      406
Circuit, electric      227 228 235 236
Coefficient, binomial      368 413 416
Coefficient, binomial, of Gauss      472
Coin, ideal      450
Component, right      323
Condition (C)      262 265 266 268 269 270 271 277 278 281 284 288 289 341
Constituent, of continued fraction      475 505
Continuation, analytic      93 94 106 107 150 158 159 249 387 567 590
Continuation, analytic, of hypergeometric series      68
Continuation, analytic, of Laplace transform      279
Continued fraction      396 474
Continued fraction of Gauss      551
Continued fraction with positive elements      483
Continued fraction, corresponding to infinite series      518 528
Continued fraction, equivalent      478 525
Continued fraction, equivalent, to infinite series      483
Continued fraction, evaluation of      475
Continued fraction, even part of      481 482
Continued fraction, improper      480
Continued fraction, odd part of      481 482
Continued fraction, reduced form of      480
Continued fraction, simple      489 490 491 495
Continued fraction, simple, nonterminating      492
Continued fraction, simple, purely periodic      497 498 499
Continued fraction, simple, ultimately periodic      493 495 496
Continued fraction, terminating      475
Contraction principle, for continued fractions      506 508
Control area, quadratic      292
Control system      230
Control unit      230
Convergence of continued fraction      475
Convergence of continued fraction with complex elements      501
Convergence of continued fraction with positive elements      483
Convergence of continued fraction, improper      475
Convergence, abscissa of      202 203 214 628
Convergence, abscissa of Dirichlet series      294 295
Convergence, linear      180
Convergence, quadratic      178 464
Convergence, set of      204
Convergence, set of absolute      200 202
Convergence, set of simple      200 202
Convergence, uniform      386
Convergence, uniform of continued fractions      505
Converging factor      617 641
Convolution      197 239 242 244 245 246
Convolution theorem      241 242 243 244 245 255
Cornu spiral      397
Correspondence      209
Correspondence, example of      210 211 213 214 215 216 217 218 219 220 221 224 225 226 228 231 232 237 243 244 247 252 253 254 256 257 259 260 282 285 324 334 335 338 339 340
Cramer’s Rule      520 521
Dahlquist, theorem of      596
Damping, of original function      217
Darboux, method of      404 446 447 450 619
Denominator, of continued fraction      477 479 483 490 491 498 501 512 516 525 532 537 542 560 561 598 604
Denominator, of continued fraction, partial      474 480
Derivative, generalized      211 213 214 221
Derivative, logarithmic      21 23 24 27
Derivative, logarithmic, of zeta function      299
Descending method, for evaluating continued fraction      476 478 485
Determinant, Jacobian      413
Determinant, Wronskian      101 104 131
Diagonal sequence      564 577
Difference equation      485 501
Difference operator, of maximum order      536
Differential equation, actual solution of      379 388
Differential equation, asymptotic solution of      378
Differential equation, Eulerian      138 388
Differential equation, formal solution of      378 379 388
Differential equation, initial value problem for      76
Differential equation, linear ordinary, with constant coefficients      220
Differential equation, scalar      76 221
Differential equation, scalar, linear      99
Differential equation, scalar, solution of      221
Differential equation, solution of      76 87
Differential equation, solution of, uniqueness of      80 88
Differential equation, special, of second order      387
Differential equations, system of      76 225
Differential equations, system of, linear      91 92
Differentiation, of original function      211 213 218
Dini’s test      266
Dirac delta function      233 234
Dirichlet problem      342
Dirichlet series      293 294 295 297 298 304 350
Dirichlet series, convergence of      294 295
Dirichlet series, derivative of      295
Dirichlet’s rule, for multiplication      296 297 350
Distribution, hypergeometric      620
Division algorithm      539 541 543 546 554 555 640
Division of original function      214
Divisor, greatest common      297 487 489
Dixon, theorem of, for hypergeometric series      51
Dixon’s formula      396
Doetsch symbol      209
Double series      83
Double series with positive terms      84
Double series, absolutely convergent      84
Double series, convergent      83
Dougall, theorem of      52 54
Drawer problem      8
Driving function      227
Eigendomain, of family of continued fractions      506 507 508 510 513 514
Eigenvalue      78 114 120 121 122 123 126 378 387
Eigenvalue of circulant matrix      415
Eisenstein’s continued fraction      528 539
Element, of continued fraction      475
Elliot, formula of      165
Elliptic integral, complete      164 165 177 178
Equation of Fuchsian type      145 146 149 151 152
Equation of the second order, special      187
Equation, confluent hypergeometric      132 194
Equation, Diophantine      489 490
Equation, hypergeometric, general      149 152 153
Equation, hypergeometric, general, reduced      154 155 158 165
Equivalence transformation      524 526 534 535 536 544
Erlang loss coefficient      416
Error function      393 614 640
Error function complement      378 397 614 630
Error function, asymptotic behavior of      73 393
Error function, Mellin — Barnes representation for      73
Euclidean algorithm      487 488
Euler polynomial      459
Euler — Maclaurin summation formula      450 455 472
Euler — Maclaurin summation formula, remainder of      458
Euler, first identity of      160 172
Euler, second identity of      160 162
Euler’s constant      25 36 446 455 456 459 460 467
Euler’s differential equation      128 338
Euler’s integral, for gamma function      30 31 32 43 45 74 247 358 390 392 402 435
Euler’s relations, for equivalent continued fractions      486
Euler’s theorem, on infinite products      10
Euler’s transformation      253 438 631
Existence theorem, for ordinary differential equations      75 86
Expansion, asymptotic      186 192 434 435 463 471 472 552 565 566 583 584 595 596 600 626 627 628 631
Expansion, asymptotic, Darboux’ method, obtained by      447
Expansion, asymptotic, enveloping      361 362 565
Exponent, characteristic      127 131 132 134 137 147 148 149 151 152 154 167 169 171
Exponential function of operator, continued fraction for      537
Exponential integral      319 353 361 580 585 622 629
Exponential integral of order n      398 405 630
Exponential polynomial      223 226 282
Exponential series, continued fraction, corresponding to      536
Exponential series, continued fraction, corresponding to partial sums of      515 559 640
Family, equicontinuous      563
Family, equicontinuous, normal      562 566 568
Family, equicontinuous, uniformly bounded      562 563 578
Fibonacci number      442 445
Filter, digital      335
Filter, input of      335
Filter, output of      335
Filter, shock response of      335
Filter, transfer function of      335
Fixed, point      494 503 504 509
Flywheel      226
Form, positive definite      598 607
Form, quadratic      597 606
Formal power series, corresponding      561
Formula, asymptotic      407 408 450
Formula, asymptotic, for Legendre polynomial      439
Fourier coefficient      262 264 270 276 448
Fourier integral      261
Fourier integral theorem      241 263 268 276
Fourier series      262 446 448
Fourier series, obtained by Heaviside expansion theorem      282 291 292
Fourier transform      267 270 272 273 275 276
Frequency admittance      231
Fresnel integral      37 397
Frobenius, method of      127 132 136 137 141 154 161 164
Fubini’s Theorem      627
Fuchs, relation of      147 150 152
Function of bounded variation      266 271
Function of exponential type      305 306 308 309 310 311 312 314 315 320 321 322 323 327 328 329 332
Function of exponential type, periodic      320
Function of semi-exponential type      314 315 316 319 320 329 332 334
Function with values in half-plane      586
Function, admitting asymptotic power series      355 361 369 370
Function, analytic, of matrix      97
Function, analytic, of several complex variables      76 85
Function, band-limited      276
Function, confluent hypergeometric      68 253 630
Function, elliptic      272
Function, entire      17 209 305
Function, entire without zeros      17 18 19
Function, entire, product representation of      17 21
Function, equivalent      207
Function, essentially uniquely determined      593
Function, generating      9 322 442 452 464
Function, hypergeometric      57 252 282 621
Function, hypergeometric, analytic continuation of      62 68 160 161 163
Function, hypergeometric, asymptotic behavior of      437
Function, hypergeometric, integral representation for      56 57
Function, hypergeometric, inverse $\mathcal{L}$-transform of      285
Function, hypergeometric, loop integrals for      60 62
Function, log-holomorphic      108 109 132 149 194 389
Function, meromorphic      531 532
Function, meromorphic, representation as quotient of entire functions      21
Function, monotonic      266
Function, non-decreasing      593 636
Function, positive symmetric      586 588 594 641
Function, summatory      52
Functional, linear positive      637
Fundamental matrix      95 97 98 99 103 104 109 114 118 124 180 387
Fundamental matrix, construction of      119
Fundamental matrix, inverse of      101
Fundamental matrix, log-holomorphic      110
Fundamental system, of scalar equation      101 126 155 156 157 161 166 192
Gamma function      24 137 247 365 377 429 430 624
Gamma function, asymptotic expansion for      377 403
Gamma function, calculation of      43
Gamma function, canonical product for      25
Gamma function, descriptive properties of      27 28
Gamma function, duplication formula for      29 35 42 72 247
Gamma function, Gauss’ definition of      28 35
Gamma function, graph of      28 42 73
Gamma function, Hankel’s representation for      33 35
Gamma function, incomplete      259 293 392 472 628
Gamma function, interpolates factorial      26
Gamma function, partial fraction decomposition of      36
Gamma function, residues of      26 27
Gamma function, Stirling’s approximation to      43 (see also “Stirling’s formula”)
Gamma function, Taylor coefficients of      446
Gamma function, Weierstrass definition of      25
Gauss bracket      486
Gauss, theorem of, for sum of hypergeometric series      48 51 53 55 161 255 621
Genus, finite      22
Geometric series      620
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