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Lorentzen L., Waadeland — Continued fractions and applications
Lorentzen L., Waadeland — Continued fractions and applications

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Название: Continued fractions and applications

Авторы: Lorentzen L., Waadeland

Аннотация:

This book is aimed at two kinds of readers: firstly, people working in or near mathematics, who are curious about continued fractions; and secondly, senior or graduate students who would like an extensive introduction to the analytic theory of continued fractions. The book contains several recent results and new angles of approach and thus should be of interest to researchers throughout the field. The first five chapters contain an introduction to the basic theory, while the last seven chapters present a variety of applications. Finally, an appendix presents a large number of special continued fraction expansions. This very readable book also contains many valuable examples and problems.


Язык: en

Рубрика: Математика/Анализ/Непрерывные дроби/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 618

Добавлена в каталог: 11.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
A posteriori truncation error bounds      63 114
A priori truncation error bounds      63 116
Absolute convergence      128
Acceleration of convergence      25 160
Adjoint recurrence relation      197
Analytic continuation      25 174
Approximant      8
Asymptotic expansion      353
Asymptotic side condition      162
Asymptotically equal      202
Attractive fixed point      103 151
Auric's theorem      207
Auric's theorem, modified      267
Backward recurrence algorithm      45
Basic hypergeometric functions      319 593
Basic hypergeometric series      318
Bauer — Muir transform      76
Bauer — Muir transformation      76
Bessel equations      542
Bessel functions $J_\nu(z)$      317 477 539 575
Bessel polynomials      477
Best rational approximation      408
Binet's formula      193
Binomial function      47
Birkhoff's method      204
Blaschke product      503
Block diagram      494
Block theorem      381
Branch point      174
Branched continued fraction      277 285
Branches      495
C-fraction      252
Canonical contraction      83
Canonical denominator      9
Canonical even part      95
Canonical numerator      9
Carleman criterion      360
Cartesian oval      142
Catalan's constant      563
Cauchy sequence      247
Chain sequence      363 463
Charlier polynomials      337
Chordal distance      43
Classical approximant      39 71
Classical value set      110
Classification of linear fractional transformations      101
Complementary error function      576
Conditional convergence set      108
Conditional general convergence set      109
Confluent hypergeometric function      311
Conjugate transformation      103
Continued fraction      7
Continued fraction algorithm      7
Continued fraction expansion      15
Continued fraction factoring algorithm      428
Contraction      83
Convergence criteria      93
Convergence of a continued fraction      8
Convergence set      108
Convolution      484
Coprime numbers      400
Correspondence      23 242
Correspondence at $z=a$      243
Correspondence at $z=\infty$      244
Coulomb wave function      579
Critical tail sequence      60
Cross ratio      62
Dawson's integral      578
Determinant formula      9 411
Difference equation      71
Differential equation      13 521
Digital filter      486
Diophantine equations      410
Directed graph      495
Disk-stability      518
Distribution function      257 342
diverge      94
Dominant solution      201
Element region      123
Ellipse, arc length of      26
Elliptic transformation      103
Elliptic type      159
Empty product      128
Empty sum      128
Equivalence transformation      72
Equivalent continued fractions      72
Error function      578
Euclidean algorithm      399
Euler fraction      307
Euler — Cauchy equation      528
Even part      84
Exponential function      281 563
Exponential integral      577
Extension      83 89
Factor base      423
Favard's theorem      345 460
Fermat factorization      420
FG-algorithm      284
Fibonacci numbers      46 193 406
Field      200 243
Fixed point      101
Formal power series      200 242
Forward recurrence algorithm      45
Forward stability      218
Fourier expansion      343
Fresnel integrals      579
Functional equation      82
Fundamental inequalities      182
G-continued fraction      226
Gamma function      199 221
Gauss fraction      295
Gauss quadrature formula      351
General binomial function      564
General convergence      43 66
General convergence set      109
General divergence      94
Generalized continued fractions      228 236
Generalized hypergeometric series      312
Golden ratio      46 562
Gragg — Warner bounds      140
Gram — Schmidt process      342
Greatest common divisor      399
Hamburger moment problem      359
Hankel determinant      341
Heine's continued fraction      320
Henrici — Pfluger truncation error bounds      139
Hermite polynomials      443
Hermitian PC-fraction      282
Hillam — Thron theorem      119
History of continued fractions      50
Hurwitz polynomial      468
Hyperbolic functions      568
Hypergeometric functions      18 292 573
Hypergeometric series      292
Identity function      101
Incomplete beta functions      581
Incomplete gamma function      230—231 576 579
Input      486
Integer part      402
Inverse hyperbolic functions      569
Inverse trigonometric functions      569
Iteration      101
Jacobi continued fraction      345 460
Jacobi's elliptic functions      583
K-periodic continued fraction      104
Khovanskii transform      89
Kronecker delta      333
Lagrange interpolation polynomial      349
Laguerre polynomials      443
Left vertex      146
Legendre functions      581
Legendre polynomials      334 442
Limit circle case      120
Limit k-periodic      150
Limit periodic continued fraction      20 150
Limit point case      116
Linear differential equation      523
Linear fractional transformation      6 62 101
Linear independence      196
Linear space      192
Linear system theory      508
Linearly independent      196
Logarithm      17 177 566
Logarithmic integral      577
Lommel polynomials      477
Loxodromic transformation      103
Loxodromic type      151
M-fraction      284
Minimal solution      201
Model reduction problem      508
Modified approximant      20 25
Modified continued fraction      44
Modified regular С-fraction      357
Modified Stieltjes fraction      357
moment      338
Moment functional      338
Moment problem      353
Moment sequence      338
Monic polynomials      333
Montessus de Ballore's theorem      385
Multipoint Pade fraction      388
Multivariate Pade approximants      389
Nested closed sets      116
Newton — Pade approximants      388
nodes      349 495
Non-trivial solution      201
Nonrecursive filter      486
Norlund fraction      304 574
Norm      243
Normal Pade table      379
Odd part      85
Order of correspondence      242
Orthogonal      332
Orthogonal polynomial sequence      339
Orthonormal polynomials      343
Oscillation property      99
Output      486
Oval sequence theorem      145
Oval theorem      141
P-fractions      281 383
Pade approximants      27 375
Pade table      375
Pade type approximants      389
Parabola sequence theorem      136
Parabola theorem      130
Parabolic transformation      103
Parabolic type      157
Parameter sequence      463
Partial denominators      7
Partial fractions      28
Partial numerators      7
PC-fraction      282 387
Pell's equation      413
Period length      101 150
Periodic continued fraction      101
Periodic tail sequence      105
Perron-tails      210
Pfaff's transformation      307
Pincherle's theorem      202 235
Pincherle's theorem, modified      265
Plasma dispersion function      577
Pochhammer symbol      199 311
Positive elements      96
Positive-definite moment functional      342
Pre value set      110
Pringsheim's theorem      30
q-hypergeometric function      319
Q-hypergeometric series      318
qd-algorithm      284
Quasi-definite moment functional      341
Ramanujan's lost notebook      595
Rational approximation      11
Recursive filter      486
Reference continued fraction      44
Reflection property      62
Regular $\delta$-fraction      281
Regular C-fraction      250
Regular continued fraction      5 401
Regular singular point      528
Regular two-dimensional C-fraction      277
Repulsive fixed point      103 151
Riccati differential equation      540
Riemaim surface      174
Riemann 1 Stieltjes integral      337
Riemann sphere      62
Riemann zeta function      561
Right Perron-tails      210
Right tail sequence      59 210
Right vertex      146
Rogers — Ramanujan continued fraction      273
RSA-cryptography      419
S-fractions      138 257
Saff — Varga's parabola theorem      464
Schur algorithm      501
Schur fraction      504
Schwarz' lemma      501
Seidel-Stem theorem      98
Separable differential equation      541
Sequence of convergence sets      109
Sequence of value sets      110
Shock response      488
Similar transformation      103
Sink node      496
Sleszyiiski — Pringsheim set      108
Sleszynski — Pringsheim's theorem      30
Solution space      191
source node      496
Speed of convergence      63
Stable filter      489
Stable polynomial      468
Stern — Stolz divergence theorem      94
Stern — Stolz series      95
Stieltjes fractions      138 453
Stieltjes moment problem      353
Stieltjes — Vitali theorem      123
Strong Stieltjes problem      363
Successive substitutions      21 259
Szego polynomial      388
T-fraction      26 245 251
tail      56
Tail sequence      59 209
Tchebychefif polynomials      230 332 442
TDCF      277
Terminating continued fraction      251
Terminating regular continued fraction      401
Thiele interpolating continued fraction      248
Thiele oscillation      105
Three-term recurrence relation      191
Transfer function      488
Transformations of continued fractions      69
Trigonometric functions      568
Trigonometric moment problem      388
Truncation error bounds      63
Truncation error estimate      182
Twin convergence sets      109
Twin value sets      111
Two-point Pade table      387
Uniform convergence set      108
Uniform general convergence set      109
Uniqueness      68
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