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| Henrici P. — Applied and Computational Complex Analysis (Vol. 2) |
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| Предметный указатель |
 fraction 525 526 529 550 560 561 597
 fraction see “S fraction”
 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  -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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