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Jones W.B., Thron W.J. — Continued fractions: Analytic theory and applications
Jones W.B., Thron W.J. — Continued fractions: Analytic theory and applications

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Название: Continued fractions: Analytic theory and applications

Авторы: Jones W.B., Thron W.J.

Аннотация:

This is an up-to-date exposition of the analytic theory of continued fractions in the complex domain with emphasis on applications and computational methods.


Язык: en

Рубрика: Математика/Анализ/Непрерывные дроби/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1980

Количество страниц: 428

Добавлена в каталог: 09.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$c_{m,n}$ determinants      189
$c_{m,n}$ determinants, Connection with $H^{(k)}_n$      226
$H^{(n)}_k$      223
$P^m_{\alpha}(z)$      214
$Q^m_{\alpha}(z)$      204
$\mathscr{H}_k^{(n)}$      261
$\mathscr{L}$: Field of fLs      148
$\mathscr{L}$: Laplace transform      366
$\mathscr{P}(\zeta)$      302
$\mathscr{R}$      151
$\mathscr{R}(\zeta)$      326
$\mathscr{S}(z)$      302
$\mathscr{T}(z)$      302
$\Pi$-fraction      317
$\Pi$-fraction, Truncation error bounds      318—319
(M, N)-normal      236
Abramowitz, M.      168 198 216 218 347 400 404
Absolute convergence of a continued fraction      126
Accelerating convergence      327—329
Akhieser, N.I.      333 404
Andrews, George E.      xxv 198 404
Anns, Edrei Theorem      238
Approximant of a continued fraction      17
Arms, Robert J.      15 222 237 239 404
Askey, R.A.      198 404
Associated continued fraction      7 129 241 388
Associated continued fraction, Algorithm      248—249
Associated continued fraction, Correspondence      242—247
Associated continued fraction, Relation to Pade table      389
Asymptotic expansion of f(z): At $z=\infty$      330
Asymptotic expansion of f(z): At z=0      333
Asymptotic expansions of continued fractions      342
Attractive fixed point      52
Auric theorem (generalized)      173
Auric, A.      148 163 404
Backward recurrence algorithm (BR-algorithm)      26 351—352
Backward recurrence algorithm (BR-algorithm), Stability      352—355
Baker, George A., Jr.      xxiv 149 185 196 197 298 320 404
Bandemer, Hans      235 404
Bankier, J.D.      46 404
Barnsley, M.      196 405
Baskervill, M.      351 413
Bauer, F.L.      15 235 241 405
Bernoulli, D.      46 405
Bernstein, F.      4 405
Bessel function $J_{\nu}(z)$      162
Bessel function $J_{\nu}(z)$, Convergence      168 183-
Bessel function $J_{\nu}(z)$, Correspondence      162—163
Bessel function $J_{\nu}(z)$, Truncation error analysis      304—305
Best element region      64
Best value region      64
Binet function J(z)      349
Birth-death process      365
Blanch, G.      298 307 351 405
Block theorem      188
Bombelli, Rafaele      1 405
Borel, E.      4 405
BR algorithm      26 351—352
Brezinski, C      xxiv 185 255 405
C-fraction      28 386
C-fraction, Correspondence      156—157
c.f.g. sequence      30
Cabannes, H.      xxiv 185 405
Cajori, Florian      19 405
Callas, N.P      383 384 405
Caratheodory, C      27 405
Cardioid theorem      134
Carleman condition      314 343
Cataldi, Pietro      1 405
Cazacu, Cabiria Andreian      131 406
Chain sequence      115 307
Chihara, T.S.      xxv 255 406
Chisholm, J.S.R.      197 406
Christoffel numbers      256
Christoffel, E.B.      8 406
Chui, C.K.      185 406
Claessens, G.      xxv 15 196 406
Classification of l.f.t.'s      48—53
Clausen, Th.      46 406
Cody, W.J.      198 406
Common, A.K.      298 406
Complementary error function      218—219 348
Computation of zeros and poles      233—235
Conditional convergence region      80
Confluent hypergeometric functions, $\Omega(a,b;z)$      212
Confluent hypergeometric functions, $\Phi(b;c;z)$      205—206
Confluent hypergeometric functions, $\Psi(c; z)$      209
Conte, Samuel D.      219 408
Continued fraction algorithm      17
Continued fraction definition      17
Continued fraction generating sequence (c.f.g. sequence)      30
Continued fraction over a normed field      22
Continued fraction representations of special function: $e^x$      24 207
Continued fraction representations of special function: $log (\frac{1 + z}{1 - z})$      203
Continued fraction representations of special function: $\frac{F(a,b;c;z)}{F(a,b+1;c+1;z)}$      200
Continued fraction representations of special function: $\frac{P^m_{\alpha}(z)}{P^{m - 1}_{\alpha}(z)}      215
Continued fraction representations of special function: $\frac{Q^m_{\alpha + n}(z)}{Q^m_{\alpha + n + 1}(n)}$      205
Continued fraction representations of special function: $\frac{\Phi(b;c;z)}{\Phi(b +1; c + 1; z)}$      206 278—281
Continued fraction representations of special function: $\frac{\Psi(c;z)}{\Psi(c +1; z)}$      209—210
Continued fraction representations of special function: $\int^x_0 \frac{dt}{1 + t^n}$      203
Continued fraction representations of special function: $\Phi(1; c; z)$      207 281—282
Continued fraction representations of special function: Arcsin z      203
Continued fraction representations of special function: Arcsinh z      204
Continued fraction representations of special function: Arctanr      24 202
Continued fraction representations of special function: Bessel function $J_{\nu}(z)$      168 183—184 211
Continued fraction representations of special function: Binet function      349
Continued fraction representations of special function: Complementary error function erfc z      218—219 348
Continued fraction representations of special function: Coulomb wave functions      215—216
Continued fraction representations of special function: Dawson integral      208 282
Continued fraction representations of special function: Error function erf z      208 282
Continued fraction representations of special function: F(a,1;c;z)      201
Continued fraction representations of special function: Fresnel integrals      208 282
Continued fraction representations of special function: Gamma function      348—350
Continued fraction representations of special function: General binomial $(1 +z)^{\alpha}$      202
Continued fraction representations of special function: Incomplete beta function      216—217
Continued fraction representations of special function: Incomplete gamma function      209 217—218 347—348
Continued fraction representations of special function: Integrals of the error function      218—219
Continued fraction representations of special function: log(l + z)      24 203
Continued fraction representations of special function: Plasma dispersion function      219
Continued fraction representations of special function: tan z      211
Continued fraction representations of special function: tanh z      211
Contraction map      301
Contraction of a continued fraction      38
Convergence neighborhood      108
Convergence neighborhood theorem      108
Convergence regions      13
Converging factors      298
Copp, George      125 406
Copson, E.T.      162 167 406
Correspondence (at $z = \infty$)      150
Correspondence (at z = 0)      148—149
Correspondence (at z = 0), Three-term recurrence relations      160—161
Coulomb wave functions      215—216
Cowling, V.F.      115 124 406
Critical point      307
Davis, P.J.      255 406
Dawson integral      208 282
Dawson, D.F.      126 128 406
de Bruin, N.G.      198 405
de Montessus de Ballore theorem      194
de Montessus de Ballore, R.      194 413
De Pree, J.D.      63 406
Dennis, J.J.      115 406
Determinant formula      20
Difference equations      20
Dominant solution      163
Donovan, A.F.      249 415
Dow, J.D.      197 416
Drew, D.M.      258 406
Dual continued fraction      56
Edrei, Albert      15 222 239 404 115 406 237 238 407
Element region      64
Elements of a continued fraction      17
Elliott, D.      298 407
Elliptic 1.f.t      52
Equivalence transformation      33
Equivalent continued fractions      31
Erdelyi, A.      198 204 214 216 407
Erdoes, P.      63 407
Error function      208 282
Euler, L.      xix 2 3 36 407
Even part      41
Extended field      21
Extension of a continued fraction      38 43
F(a,b;c;z)      199
Fair, Wyman      xxv 407
Farinha, Joao      63 126 407
Favard, J.      254 407
FG algorithm      268—269
FG algorithm, Computation of zeros and poles      273—275
FG table      268
Field, David A.      298 302 304 320 407
fLs      148
Ford, L.R.      27 407
Formal Laurent series (fLs)      148
Formal Newton series (fNs)      195
Formal power series (fps)      148
Forward recurrence algorithm (FR algorithm)      26 351
Fps      148
FR algorithm      26 351
Frank continued fraction      392
Frank, Evelyn      198 221 258 283 295 392 407
Franzen, N.R.      151 408
Fresnel integrals      208 282
Fried, Burton D.      219 408
Frobenius, G.      7 185 408
Function ineromorphic in D      131
Fundamental inequalities      125
G-fraction      335 390
g-fraction, Convergence      138
g-fraction, Truncation error bounds      318—319
g-table      240
Gallucci, Michael A.      196 408
Galois theorem (generalized)      56
Galois, E.      3 46 408
Gamma function      348—350
Gammel, John L.      xxiv 185 404
Gargantini, I.      235 408
Gauss continued fraction      200
Gauss, C.F.      3 5 14 147 408
Gaussian quadrature      255—256
Gautschi, Walter      xxv 14 148 163 167 198 214 215 217 218 249 258 408
General T-fraction      130 257 390—391
General T-fraction, Connection with FG algorithm      266—272
General T-fraction, Connection with M-fraction      391
General T-fraction, Convergence      140 141 142 275—276
General T-fraction, Correspondence      258—266
General T-fraction, Relation to two-point Pade table      391—392
General T-fraction, Representation of functions      275—282
Generate (a sequence of 1.f.t.'s)      27
Gilewicz, Jacek      xxiv 185 408
Gill, John      63 298 329 408
Glaisher, J.W.L.      298 328 408
Gragg, W.B.      298 317 319 320 408 185 188 189 194 197 237 248 250 409
Graves-Morris, P.R.      xxiv 185 197 409
Grommer, J.      331 409
Grundy, R.E.      258 409
Guenther, S.      46 409
H-fraction      335 387
Haddad, Hadi M.      115 409
Hag, K.      256 380 409
Hamburger, H.      9 15 90 331 409
Hamel, G.      298 409
Hankel determinants $H^{(n)}_k$      223
Hankel determinants $H^{(n)}_k$, Connection with $c_{m,n}$      226
Hankel determinants $\mathscr{H}_k^{(n)}$      261
Hayden, T.L.      xxv 9 126 301 307 328 409 298 385 410
Heilennann, J.B.H.      7 410
Hellinger, E.      106 410
Henrici, P.      xxiii—xxv 101 148 198 228 229 234 235 275 283 295 298 313 320 330 333 349 350 387 399 410
Hermite interpolation      14 186
Herschel, J.F.W.      19 410
Hildebrand, F.B.      255 410
Hillam, K.L.      94 410
Hille, E      27 89 410
Householder, A.S      235 410
Hovstad, R.M.      256 378 379 410
Hurwitz (or stable) polynomial      283
Hurwitz (or stable) polynomial, Necessary and sufficient conditions      290 293 295—296
Hurwitz criterion for stability      295—296
Hurwitz, A.      283 410
Huygens, Christian      2 3 410
Hyperbolic l.f.t.      52
Hypergeometric function F(a, b; c; z)      199
Hypergeometric function F(a, b; c; z), Continued fraction representation      199—202
Hypergeometric series      5
Idempotent      69
Ince, E.Lindsay      198 258 410
Inclusion region      297—299
Incomplete beta function      216—217
Incomplete gamma function      209 217—218 347—348
Indifferent fixed point      52
Integral part of positive para-odd function      287
Integral representations of continued fractions      337—340
Integrals of the error function      218—219
Isihara, A.      197 410
Ismail, M.E.H.      198 404
J-fraction      129 249 389
J-fraction, Connection with associated continued fraction      249—250
J-fraction, Connection with orthogonal polynomials      250—255
Jacobi identity      229
Jacobi, C.G.J.      4 411
Jefferson, Thomas H.      256 298 316 380 411
Jensen, J.L.W.V.      90 411
Johnson, G.D.      197 409
Jones, William B.      196 302 304 408 xxiv 13 14 15 60 62 68 69 71 80 94 98 99 105 106 107 115 124 125 126 147 181 185 197 256 257 261 271 272 274 298 305 308 310 312 322 325 331 342 351 353 358 365 369 382 411
Jordan, J.Q.      125 412
Kahl, E.      46 412
Karlin, S.      365 412
Karlsson, J.      196 197 412
Khintchine, A.      4 5 412
Khovanskii, A.N.      xxiii xxv 198 412
Kummer function      206
l.f.t.      26
Lagrange, J.L.      5 412
Laguerre, E.      6 8 412
Lambert, J.H.      5 412
Landsberg, G.      46 412
Lane, R.E.      9 46 67 126 412
Lange, L.J.      13 115 124 298 324 412
Larkin, F.W.      196 412
Legendre functions of the first kind $P^m_{\alpha}(z)$      214
Legendre functions of the second kind $Q^m_{\alpha}{z)$      204
Legendre, A.M.      3 6 412
Lehner, J.      27 412
Leighton, W.      46 404 115 124 406 13 76 99 125 134 156 181 413
Levinson, N.      283 413
Limit periodic continued fraction      107
Limit periodic continued fraction, $K(a_n/1)$      113
Limit-circle case      66
Limit-point case      66
Linear fractional transformation (l.f.t.)      26
Liouville, J.      4 413
Loxodromic l.f.t.      52
Luke, Yudell, L.      198 298 413
M(b; c; z)      206
M-fraction      130 391
Macon, N.      351 413
Magnus, Arne      16 271 272 274 365 369 411 63 156 193 390 413
Mall, J.      90 413
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