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| Авторизация |
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| Поиск по указателям |
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| Henrici P. — Applied and Computational Complex Analysis (Vol. 2) |
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| Предметный указатель |
Sampling theorem 276
Scalar equation of second order 102
Scalar equation, of higher order 124 221
Scalar equation, reduction to special form 103
Schur form of matrix 120
Schwarz formula 586 587
Schwarz inequality 31
Sequence, asymptotic 432 433 434 440 455
Sequence, coasymptotic 441
Series, asymptotic 352 617 635
Series, binomial 45 421 447 535
Series, confluent hypergeometric 133 515
Series, confluent hypergeometric, asymptotic behavior of 70 71
Series, confluent hypergeometric, continued fraction corresponding to 535
Series, corresponding 530
Series, defenition of 414
Series, enveloping 161 168 412
Series, formal logarithmic 380
Series, hypergeometric, analytic continuation of 66 163
Series, hypergeometric, contiguous 48
Series, hypergeometric, formula of Gauss, for value z 1 48 51
Series, hypergeometric, linear transrorm of 163
Series, hypergeometric, quadratic transrorm of 165
Series, hypergeometric, RITZ fraction corresponding to 533
Series, initially convergent 352
Series, log-exponential 189
Series, semiconvergent 352
Shock response 232 233 234 235 237 242
Shock response of digital filter 335
Sievert integral 398
Similarity 211
Sine function, product representation for 5 23 24
Singular point, irregular 109 125 378
Singular point, of first kind 114 124 125 126 131 132 144 146 148 149 180
Singular point, of second kind 180
Singular point, regular 109 125 126
Singular point, virtual 319
Singular points, set of 318
Singularity 311 319
Singularity, essential 105 369
Singularity, isolated, of linear system 105
Singularity, rank of 180 378
Singularity, removable 541 543
Singularity, subtracted, method of 448
Singularity, virtual 319
SITZ fraction 551 552 553 555 559 561
SITZ fraction, n-terminating 555
Solution, formal 116 118 127 131 184 186
Solution, linearly independent 95 130
Solution, log-holomorphic 111
Solution, normal 181
Solution, trivial 94
Sommerfeld’s integral, for Bessel function 344 347 349 350 422
Square root, of positive definite matrix 413
st 585 586 594 596 602
Stability test function 559 560
Steepest descent, line of 417 420 423
Steepest descent, method of 416 419 444 472
Step function 238 570 577
Stieltjes fraction see “S fraction”
Stieltjes integral 569 570 572 573 581 585 609 641
Stieltjes transform 337 339 553 554 555 556 568 580 581 586 594 596 617 627
Stieltjes transform, inversion of 590
Stirling number 442
Stirling’s formula 37 42 45 47 48 52 64 65 68 71 73 137 248 307 320 352 357 377 402 436 467 468 608 622 623 625 628
Stokes phenomenon 387 388
| Subdivision 569 571 572 574
Successive approximations 77 103 246
Sum, log-exponential 181 182 193
Sum, partial, of double series 83
Summation formula of Plana 38 300 329 330
Summation formula of Poisson 270 271 272—276 322 350
Summation, by parts 251 294
Support function of convex hull of singularities 312 314
Support function of convex set 312
Symmetry principle 553
system 227
System, fundamental 95
System, induced 143
System, linear 229
System, stable 230 231
Tauberian theorem 287 290
Taylor’s Formula 245
Taylor’s formula with remainder 353 398
Term, of double series 83
Theta function 272
Three-body problem, restricted 194
Transfer function 228 229.
Transform of Goursat 176
Transform, cubic 176
Transform, quadratic 165 172 175 179 253 449
Transformation of variable 101 104 105
Transformation, inverse 206
Transitional region 430
Translation, of original function 216
Trapezoidal formula 452 457
Trapezoidal value, of definite integral 274 275 457 458 461
Truncation error, of continued fraction 603 618
Type of rational function 519
Type of rational function, precise 545 546
Type of rational function, semi-exponential 389
Unit ball, n-dimensional, surface area of 61
Unit ball, n-dimensional, volume of 60
Value function 565 566 577 602 610 638
Value function, generalized 565 566 568 577 578 579 582 611 612 637
Vandermonde formula 49
Vandermondian determinant 148
Variables, separation of 340 341 342 344
Variation of constants 99 101 221 237 381
Variation, bounded 278
VF 585 596 608
Vitali’s theorem 566
Wallis’ formula 5
Wallis’ product 47
Wall’s criterion, for stability 560
Watson — Doetsch lemma 290 389 392 393 394 397 399 413 418 419 422 435 627 628 631
Watson — Doetsch lemma, extension of 399 401
Watson’s lemma see “Watson — Doetsch lemma”
Weber and Schafheitlin, integrals of 255 260 350
Weierstrass approximation theorem 207
Weierstrass approximation theorem, Lebesgue’s proof of 45
Weierstrass double series theorem 87 204 530
Weighing function 233
Weight function 600
Whittaker function of the second kind 191 254 394 397 398 630
Whittaker function, inverse Laplace transform of 285
Whittaker function, of the first kind 191
Whittaker, differential equation of 191
Worpitzky’s theorem 506 508 509 513 530
Z transform 322 327 332 334 335 336 350
Zeta function, functional equation for 305
Zeta function, of Riemann 16 295 296 297 299 300 301 460
Zeta function, zeros of 304 305
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