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Baker G.A., Graves-Morris P. Pade approximants (vol. 2)
Baker G.A., Graves-Morris P.  Pade approximants (vol. 2)







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: Pade approximants (vol. 2)

: Baker G.A., Graves-Morris P.

:

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.


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ed2k: ed2k stats

: 1981

: 215

: 06.04.2005

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$\eta$-Algorithm      I: 8084
$\varepsilon$-Algorithm      I: 7680 8490
$\varepsilon$-Algorithm for vector sequences      II: 55
$\varepsilon$-Algorithm, generalized      II: 1416
A-stability      II: 151
Acceleration of convergence      I: 1617 6990
Accuracy, numerical      I: 5865
Accuracy-through-order      I: 12
Aitkens $\Delta^2$ method      I: 6974
Algorithms for rational interpolation      II: 617
Anharmonic oscillator      II: 170171
Arzelas theorem      I: 175
Associated continued fraction      I: 127
Asymptotic convergence      I: 200
Asymptotic expansion      I: 221
Backward recurrence method      I: 115
Baker algorithm      I: 66
Baker definition      I: 2122 II:
Baker Gammel approximants      II: 2132 63
Baker Gammel approximants, asymptotic      II: 3031
Baker, Gammel and Wills, conjecture of      I: 286
Baker, Gammel and Wills, theorem of      I: 3233
Beardons theorems      I: 237
Behte Salpeter equation      II: 108113
Bigradients      I: 3742 136137
Bigradients, polynomial      I: 39
Binomial function      I: 139 144
Biorthogonal algorithm      II: 7679
BLOCKS      I: 2431
C(L/M), definition of      I: 21
C-fraction      I: 127
C-table      I: 2223 29 31
Calculation of Pade approximants, algebraic      I: 814 4348 6668
Calculation of Pade approximants, numerical      I: 6168
Canterbury approximants      II: 4145
Capacity      I: 274284
Cardioid theorem      I: 151
Carlemans criterion for Hamburger series      I: 223
Carlemans criterion for Stieltjes series      I: 200202
Carlemans criterion, application of      II: 169
Cartans lemma      I: 274
Cauchy Binet formula      I: 239240
Cauchy Jacobi problem      II: 1
Characteristic function      II: 128132
Chebychev      see Tchebyscheff
Chisholm approximants      II: 4143
Chordal metric      I: 256263
Clenshaw Lord algorithm      II: 5860
Coefficient problem      I: 65 II:
Collocation      II: 138145
Complementary error function      I: 140 144
Continued fractions      I: 103157
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: 104105 107
Continued fractions, divergence condition for      I: 148
Continued fractions, elements of      I: 104 119
Continued fractions, equivalence transformation of      I: 105107
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: 117138
Continued fractions, summation formula      I: 115116
Continued fractions, terminating      I: 104
Convergence in capacity      I: 274284
Convergence in measure      I: 263274
Convergence of row sequences      I: 238 261
Convergents      I: 104 111112 117119
Cordelliers identity      I: 88
Crank Nicholson methods      II: 145153
Critical point methods      I: 5557 5961 II: 178
D(m, n), definition of      I: 162
D-log Pade approximants      I: 55 II:
Dawson integral      I: 141
Dawson integral, generalized      II: 19
de Montessuss theorem      I: 241252
de Montessuss theorem, generalization of      I: 254 II:
Defect      I: 5355 5859
Deficiency index      I: 20
Density function, construction of      I: 180181
Determinancy of moment problem      I: 17 179 193 197207
Determinantal formulas for Pade approximants      I: 48 4348
Determinantal identities for Stieltjes series coefficients      I: 165166
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: 145153
Divergence condition      I: 148 156157
Divided differences      II: 2
Duality      I: 31 236
Equicontinuity      I: 174176
Equicontinuous sequences      I: 210 261
Equivalence transformation      I: 105106
Error formula for Pade approximants of Hamburger series      II: 128129
Error formula for Pade approximants of Stieltjes      I: 185 189193 II:
Error formula for Pade approximation      I: 6 250
Error formula for Pade approximation, from variational principles      II: 103106
Error function      I: 141 II:
Essential singularity      I: 49
Euclidean algorithm      I: 66 134135
Euler Maclaurin sum formula      II: 130
Eulers corresponding fraction      I: 137139
Eulers function and series      I: 1718 200202
Eulers recurrence theorem      I: 106
Eulers summation formula      I: 115116
Existence of Pade approximants      I: 27
Exploding vacuum      II: 166167
Exponential approximants      II: 28
Exponential function, continued fractions for      I: 139143
Exponential function, Pade approximants for      I: 814
Exponential function, Saff Varga theorems for      I: 229233
Exponential integral, continued fraction for      I: 140 144 II:
Exponential integral, first order      I: 186
Extended Stieltjes series      see Hamburger series
Factorization      II: 43
Fisher approximants      II: 45
Forward recurrence method      I: 114115
Frobenius definition      I: 20 22
Frobenius identities      I: 85 9093
Gamma function, Binets formula for      I: 202205
Gammel Guttman Gaunt Joyce approximants      II: 3336
Gammels counterexample      I: 285
Gaussian quadrature      II: 127132
General C-fraction      I: 129
Gnomic theory      II: 74
Greens functions, bound-state      II: 113
Greens functions, bound-state, partial wave, free      II: 89
Greens functions, bound-state, partial wave, Jost solution      II: 90
Greens functions, bound-state, partial wave, momentum space      II: 114
Greens functions, bound-state, partial wave, standing wave, free      II: 89
Greens functions, bound-state, S-wave, exponential potential      II: 98
Greens functions, bound-state, three-dimensional, free      II: 81
Greens functions, bound-state, three-dimensional, relativistic, free      II: 108
Greens functions, bound-state, three-dimensional, relativistic, standing wave, free      II: 109
Greens functions, bound-state, three-dimensional, standing wave, free      II: 85
Gregorys series      I: 78 81
Hadamards determinant theorem      I: 3942 243
Hamburger functions as real J-fractions      I: 225
Hamburger moment, definition of      I: 208 222
Hamburger series, definition of      I: 208 222
Hamburgers theorem      I: 221
Hankel determinant      I: 7 41
Hankel matrix, condition number of      I: 6465
Hardys puzzle      I: 7880
Hausdorff measure, $\alpha$-dimensional      I: 283
Hausdorff moment problem      I: 193196
Herglotz functions      I: 225227
Hermites formula      I: 250 II:
High field expansions      II: 179
Hilbert space methods      II: 46 6872 103107
Homographic invariants      I: 3233 II: 45 53
Hughes Jones approximants      II: 4345
Hyperbolic tangent      I: 139 143144
Hypergeometric functions      I: 141147 197198
Hypergeometric functions, $_1F_1(\dot)$, Pade approximants of      I: 43 47 142147 154 II:
Hypergeometric functions, $_2F_0(\dot)$, Pade approximants of      I: 43 47 141147 154155
Hypergeometric functions, $_2F_1(\dot)$, Pade approximants of      I: 4347 141147 156
Identities for neighboring approximants      I: 9096
Inclusion regions      I: 171 206
Incomplete gamma function      I: 140 141 145 II:
Inequalities for density function      II: 132138
Inequalities for moments      I: 186
Integer moment problem      I: 196197
Integral equations      II: 6479
Interlacing      I: 168169 210 227 II:
Invariance, homographic      I: 3233 II: 45 53
Inverse hyperbolic tangent      I: 140 144
Inverse tangent      I: 139 144 II:
J-fraction      I: 128
Jost method      II: 121122
K-matrix      II: 85 107 110112
Kernels, compact      II: 6772
Kernels, compact, completely continuous      II: 6772
Kernels, compact, finite rank      II: 6567 72
Kroneckers algorithm      I: 66 II:
L-stability      II: 151
Laguerre polynomials      I: 186
Laguerres method      II: 165
Lanczos biorthogonal method      II: 76
Lanczos T-method      II: 138145
Laplace transform, inversion of      II: 153155
Lattice-cutoff field theory      II: 176178
Laurents theorem      I: 49
Le Roy function      II: 32
Lemniscates      I: 274284
Lippman Schwinger equation      II: 8283 113
Logarithmic capacity      I: 283
Markov problem      II: 137
Matrix Pade approximants      II: 5056
Measure, convergence in      I: 263
Meromorphic functions, convergence of sequences of      I: 259
Mittag Leffler star      I: 50
Moment bounds      I: 186
Moment method      II: 46
Moment problems      I: 178179
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:
Multi-index      I: 239
Multipoint Pade approximation      I: 254 II:
Multipole      I: 49
Multivariable approximants      II: 4050
N-point Pade approximants      II: 131
Natural logarithm      I: 140 144
Newton interpolating polynomials      II: 23
Newton Pade approximants      II: 131
Nuttalls compact form      I: 16
Nuttalls theorem      I: 269
Orthogonal polynomials      I: 8286 209210 255256
Osculatory rational interpolation      II: 131
P-fraction      I: 130131
Pade approximant      I: 1288 II:
Pade denominator, definition of      I: 4
Pade equations      I: 23
Pade numerator, definition of      I: 6
Pade table      I: 78 2731
Pade Tchebycheff approximants      II: 5662
Pade-Borel approximation      II: 2930
Pade-Fourier approximants      II: 6263
Pade-Frobenius definition      I: 20 22
Pade-Legendre series      II: 2129
Parabola theorem for continued fractions      I: 150
Parabola theorem of Saff and Varga      I: 229232
Paradiagonal sequences      I: 236
Peres model      II: 167
Perrons counterexample      I: 238
Pion Pion scattering      II: 172176
Poles and zeros of Pade approximants      I: 31 4959 96102 126 166 263
Poles and zeros of Pade approximants for Hamburger functions      I: 209 227
Poles and zeros of Pade approximants for Stieltjes functions      I: 186 193
Poloids      II: 175
Polya frequency series      I: 227235
Pommerenkes theorem      I: 271
Potential scattering      II: 79126
Projection techniques      II: 7279
Prong method      II: 4344
Pryms function      I: 140 147
Q. D. algorithm      I: 99 125126
Q. D. algorithm for T-fractions      II: 20
Q. D. algorithm, generalized      II: 1314
Q. D. Table      I: 99 125126
Quadratic approximants      II: 3637 49
Quadrature      II: 127132
Quantum theory, connection with      II: 79126
Quasi-analytic functions      I: 51
Ratio method      II: 33
Rational approximation      II: 155162
Rational interpolation      II: 131
Ray sequences      I: 191
Real J-fractions      I: 128 225
Real symmetric functions      I: 160161 180
Regular C-fraction      I: 127
Reliability      I: 63 132 II:
Rhombus rule      I: 77 81
Riccati equation, Pade approximants for      II: 162165
Riemann sphere      I: 257
Root problem      I: 96102
Rouches Theorem      I: 279
Runges theorem      II: 158159
S-fraction      I: 127128 165 206
S-matrix, partial wave      II: 89 91
Saffs theorem      I: 254
Scattering theory, quantum mechanical      II: 8092
Schwarzs lemma      I: 189 192
Sectorial theorem of Saff and Varga      I: 229
Seidels theorem      I: 148150
Sequence, acceleration of convergence of      I: 1617 6990
Sequence, column      I: 30
Sequence, diagonal      I: 17 32 35
Sequence, paradiagonal      I: 30
Sequence, row      I: 30
Series analysis      I: 5557 5961 II:
Series, acceleration of convergence of      I: 1617 6990
Shafer approximants      II: 3637
Single-sign potentials      II: 106114
Singular potentials      II: 120126
Spherical convergence      I: 256263
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
Stieltjes series, S-fraction for      I: 165
Sturm sequence      I: 167
Sylvesters theorem      I: 23 167
T-fractions      I: 138 II:
T-matrix      II: 8182 103 172176
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, Trudis theorem      I: 42
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