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Baker G.A., Graves-Morris P. Ч Pade approximants (vol. 1)
Baker G.A., Graves-Morris P. Ч Pade approximants (vol. 1)



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Ќазвание: Pade approximants (vol. 1)

јвторы: Baker G.A., Graves-Morris P.

јннотаци€:

The authors cover applications to statistical mechanics and critical phenomena. There are newly extended sections devoted to circuit design, matrix Pade approximation, computational methods, and integral and algebraic approximants.


язык: en

–убрика: ћатематика/јнализ/Ќепрерывные дроби/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1981

 оличество страниц: 325

ƒобавлена в каталог: 05.04.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$\eta$-Algorithm      I:80Ч84
$\varepsilon$-Algorithm      I:76Ч80 84Ч90
$\varepsilon$-Algorithm, for vector sequences      II:55
$\varepsilon$-Algorithm, generalized      II: 14Ч 16
${}_1F_1(\cdot)$. Pade approximants of      I:43 47 142Ч147 154 II:19
${}_2F_1(\cdot)$. Pade approximants of      I:43Ч47 141Ч147 156
${}_2F_n(\cdot)$. Pade approximants of      I:43 47 141Ч147 154Ч155
A-stability      II:151
Acceleration of convergence      I:16Ч17 69Ч90
Accuracy, numerical      I:58Ч65
Accuracy-through-order      I:1Ч2
Aitken's $\Delta^2$ method      I:69Ч74
Algorithms for rational interpolation      II:6Ч17
Anharmonic oscillator      II:170Ч171
Arzela's theorem      I:175
Associated continued fraction      1.127
Asymptotic convergence      I:200
Asymptotic expansion      I:221
Backward recurrence method      I:115
Baker algorithm      I:66
Baker definition      I:21Ч22; II:52
Baker Ч Gammel approximants      II:21 Ч32 63
Baker Ч Gammel approximants, asymptotic      II:30Ч31
Baker, Gammel and Wills, conjecture of      I:286
Baker, Gammel and Wills, theorem of      I:32Ч33
Beardon's theorems      I:237
Behte Ч Salpeter equation      II: 108Ч113
Bigradients      I:37Ч42 136Ч137
Bigradients, polynomial      I:39
Binomial function      I:139 144
Biorthogonal algorithm      II:76Ч79
BLOCKS      I:24Ч31
C(L/M), definition of      I:21
C-fraction      I:127
C-table      I:22Ч23 29 31
Calculation of Pade approximants, algebraic      I:8Ч14 43Ч48 66Ч68
Calculation of Pade approximants, numerical      I:61Ч68
Canterbury approximants      II:41Ч45
Capacity      I:274Ч284
Cardioid theorem      I:151
Carleman's criterion, application of      II:169
Carleman's criterion, for Hamburger series      I:223
Carleman's criterion, for Stieltjes series      I:200Ч202
Cartan's Lemma      I:274
Cauchy Ч Binet formula      I:239Ч240
Cauchy Ч Jacobi problem      II: 1
Characteristic function      II:128Ч132
Chebychev      see Tchebyscheff
Chisholm approximants      II:41Ч43
Chordal metric      I:256Ч263
Clenshaw-Lord algorithm      II:58Ч60
Coefficient problem      I:65; II:7
Collocation      II:138Ч145
Complementary error function      I:140 144
Continued fractions      I:103Ч157
Continued fractions, associated      I:127
Continued fractions, contraction of      I:127 147
Continued fractions, convergents of      see convergents
Continued fractions, corresponding      I:127
Continued fractions, definition      I:104Ч105 107
Continued fractions, divergence condition for      I:148
Continued fractions, elements of      I:104 119
Continued fractions, equivalence transformation of      I:105Ч107
Continued fractions, periodic      I:117 138
Continued fractions, recurrence relations for      I:106 109 135
Continued fractions, regular corresponding      I:127
Continued fractions, repeating      I:117Ч138
Continued fractions, summation formula      I:115Ч116
Continued fractions, terminating      I:104
Convergence, in capacity      I:274Ч284
Convergence, in measure      I:263Ч274
Convergence, of row sequences      I:238 261
Convergents      I:104 111Ч112 117Ч119
Cordellier's identity      I:88
Crank Ч Nicholson methods      II: 145Ч153
Critical point methods      I:55Ч57 59Ч61 II:32Ч40 178
D(m, n), definition of      I:162
D-log Pade approximants      I:55; II:33
Dawson integral      I:141
Dawson integral, generalized      II:19
de Montessus's theorem      I:241Ч252
de Montessus's theorem, generalization of      I:254; II:161
Defect      I:53Ч55 58Ч59
Deficiency index      I:20
Density function, construction of      I:180Ч181
Determinancy of moment problem      I:17 179 193 197Ч207
Determinantal formulas for Pade approximants      I:4Ч8. 43Ч48
Determinantal identities for Stieltjes series coefficients      I:165Ч166
Determinantal inequalities      I:227 235
Determinantal inequalities, for Hamburger series coefficients      I:227 235
Determinantal inequalities, for Stieltjes series coefficients      I:208 209
Diagonal sequences      I:236
Diffusion processes      II: 145Ч153
Divergence condition      I:148 156Ч157
Divided differences      II:2
Duality      I:31 236
Equicontinuity      I:174Ч176
Equicontinuous sequences      I:210 261
Equivalence transformation      I:105Ч106
Error formula for Pade approximants of Hamburger series      II:128Ч129
Error formula for Pade approximants of Stieltjes      I:185 189Ч193;
Error formula for Pade approximation      I:6 250
Error formula from variational principles      II:103Ч106
Error function      I:141 II:19Ч20
Essential singularity      I:49
Euclidean algorithm      I:66 134Ч135
Euler Ч Maclaurin sum formula      II:130
Euler's corresponding fraction      I:137Ч139
Euler's function and series      I:17Ч18 200Ч202
Euler's recurrence theorem      I:106
Euler's summation formula      I:115Ч116
Existence of Pade approximants      I:27
Exploding vacuum      II:166Ч167
Exponential approximants      II:28
Exponential function, continued fractions for      I:139Ч143
Exponential function, Pade approximants for      I:8Ч14
Exponential function, Saff Ч Varga theorems for      I:229Ч233
Exponential integral, continued fraction for      I:140; 144 II:164Ч165
Exponential integral, first order      I:186
Extended Stieltjes series      see Hamburger series
Factorization      II:43
Fisher approximants      II:45
Forward recurrence method      I:114Ч115
Frobenius definition      I:20 22
Frobenius identities      I:85 90Ч93
Gamma function, Binet's formula for      I:202Ч205
Gammel Ч Guttman Ч Gaunt Ч Joyce approximants      II:33Ч36
Gammel's counterexample      I:285
Gaussian quadrature      II:127Ч132
General C-fraction      I:129
Gnomic theory      II:74
Green's functions, bound-state      II:113
Green's functions, partial wave, free      II:89
Green's functions, partial wave, Jost solution      II:90
Green's functions, partial wave, momentum space      II:114
Green's functions, partial wave, standing wave, free      II:89
Green's functions, S-wave, exponential potential      II:98
Green's functions, three-dimensional, free      II:81
Green's functions, three-dimensional, relativistic, free      II: 108
Green's functions, three-dimensional, relativistic, standing wave, free      II:109
Green's functions, three-dimensional, standing wave, free      II:85
Gregory's series      I:78 81
Hadamard's determinant theorem      I:39Ч42 243
Hamburger functions as real J-fractions      I:225
Hamburger moment, definition of      I:208 222
Hamburger series, definition of      I:208 222
Hamburger's theorem      I:221
Hankel determinant      I:7 41
Hankel matrix, condition number of      I:64Ч65
Hardy's puzzle      I:78Ч80
Hausdorff measure, a-dimensional      I:283
Hausdorff moment problem      I:193Ч196
Herglotz functions      I:225Ч227
Hermite's formula      I:250; II:2
High field expansions      II:179
Hilbert space methods      II:46 68Ч72 103Ч107
Homographic invariance      I:32Ч33 II:42Ч43 45 53
Hughes Jones approximants      II:43Ч45
Hyperbolic tangent      I:139 143Ч144
Hypergeometric functions      I:141Ч147 197Ч198
Identities for neighboring approximants      I:90Ч96
Inclusion regions      I:171 206
Incomplete gamma function      I:140 141 145 II:19
Inequalities, for density function      II:132Ч138
Inequalities, for moments      I:186
Integer moment problem      I:196Ч197
Integral equations      II:64Ч79
Interlacing      I:168Ч169 210 227;
Invariance, homographic      I:32Ч33; II:42Ч43 45 53
Inverse hyperbolic tangent      I:140 144
Inverse tangent      I:139 144;
J-fraction      I:128
Jost method      II:121Ч122
K-matrix      II:85 107 110Ч112
Kernels, compact      II:67Ч72
Kernels, completely continuous      II:67Ч72
Kernels, finite rank      II:65Ч67 72
Kronecker's algorithm      I:66; II:7
L-stability      II:151
Laguerre polynomials      I:186
Laguerre's method      II: 165
Lanczos $\tau$-method      II:138Ч145
Lanczos biorthogonal method      II:76
Laplace transform, inversion of      II: 153Ч155
Lattice-cutoff field theory      II:176Ч178
Laurent's theorem      I:49
Le Roy function      II:32
Lemniscates      I:274Ч284
Lippman Ч Schwinger equation      II:82Ч83 113
Logarithmic capacity      I:283
Markov problem      II:137
Matrix Pade approximants      II:50Ч56
Measure, convergence in      I:263
Meromorphic functions, convergence of sequences of      I:259
Mittag Ч Leffler star      I:50
Moment bounds      I:186
Moment method      II:46
Moment problems      I:178Ч 179
Moment, definition of Hamburger      I:208 222
Moment, definition of Hausdorff      I:195
Moment, definition of Stieltjes      I:158
Moments, bounds for      I:186; II:132Ч138
Multi-index      I:239
Multipoint Pade approximation      I:254; II:1Ч31
Multipole      I:49
Multivariable approximants      II:40Ч50
N-point Pade approximants      II:1Ч31
Natural logarithm      I:140 144
Newton interpolating polynomials      II:2Ч3
Newton Ч Pade approximants      II:1Ч31
Nuttall's compact form      I:16
Nuttall's theorem      I:269
Orthogonal polynomials      I:82Ч86 209Ч210 255Ч256
Osculatory rational interpolation      II:1Ч31
P-fraction      I:130Ч131
Pade approximant      I:1Ч288; II:1Ч180
Pade denominator, definition of      I:4
Pade equations      I:2Ч3
Pade numerator, definition of      I:6
Pade table      I:7Ч8 27Ч31
Pade Ч Borel approximation      II:29Ч30
Pade Ч Fourier approximants      II:62Ч63
Pade Ч Frobenius definition      I:20 22
Pade Ч Legendre series      II:21Ч29
Pade Ч Tchebycheff approximants      II:56Ч62
Parabola theorem for continued fractions      I:150
Parabola theorem of Saff and Varga      I:229Ч232
Paradiagonal sequences      I:236
Peres model      II:167
Perron's counterexample      I:238
Pion-Pion scattering      II: 172Ч176
Poles and zeros for Hamburger functions      I:209 227
Poles and zeros for Stieltjes functions      I:186 193
Poles and zeros of Pade approximants      I:31 49Ч59 96Ч102 126 166 263
Poloids      II:175
Polya frequency series      I:227Ч235
Pommerenke's theorem      I:271
Potential scattering      II:79Ч126
Projection techniques      II:72Ч79
Prong method      II:43Ч44
Prym's function      I:140 147
Q. D. algorithm      I:99 125Ч126
Q. D. algorithm, for T-fractions      II:20
Q. D. algorithm, generalized      II:13Ч14
Q. D. Table      I:99 125Ч126
Quadratic approximants      II:36Ч37 49
Quadrature      II:127Ч132
Quantum theory, connection with      II:79Ч126
Quasi-analytic functions      I:51
Ratio method      II:33
Rational approximation      II:155Ч162
Rational interpolation      II:1Ч31
Ray sequences      I:191
Real J-fractions      I:128 225
Real symmetric functions      I:160Ч161 180
Regular C-fraction      I:127
Reliability      I:63 132:
Rhombus rule      I:77 81
Riccati equation, Pade approximants for      II:162Ч165
Riemann sphere      I:257
Root problem      I:96Ч102
Rouche's theorem      I:279
Runge's theorem      II:158Ч159
S-fraction      I:127Ч128 165 206
S-fraction for      I:165
S-matrix, partial wave      II:89 91
Saff s theorem      I:254
Scattering theory, quantum mechanical      II:80Ч92
Schwarz's lemma      I:189 192
Sectorial theorem of Saff and Varga      I:229
Seidel's theorem      I:148Ч150
Sequence, acceleration of convergence of      I:16Ч17 69Ч90
Sequence, column      I:30
Sequence, diagonal      I:17 32 35
Sequence, paradiagonal      I:30
Sequence, row      I:30
Series analysis      I:55Ч57 59Ч61;
Series, acceleration of convergence of      I:16Ч17 69Ч90
Shafer approximants      II:36Ч37
Single-sign potentials      II:106Ч114
Singular potentials      II:120Ч126
Spherical convergence      I:256Ч263
Star Identity      I:23
Stieltjes function      I:158 208
Stieltjes function, definition of      I:158 221
Stieltjes function, numerical calculation of      I:64
Stieltjes inversion formula      I:221
Stieltjes series      I:158 208
Stieltjes series, definition of      I:158 221
Stieltjes series, example of      I:161
Stieltjes series, inequalities for Pade approximants of      I:170
Sturm sequence      I:167
Sylvester's theorem      I:23 167
T-fractions      I:138; II:17Ч21
T-matrix      II:81Ч82 103 172Ч176
T-matrix, partial wave      II:89
T-matrix, Toeplitz matrix      I:67
T-matrix, Totally monotone sequence      I:195
T-matrix, Totally positive series      I:228
T-matrix, Trudi's theorem      I:42
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