| Preface to the Second edition |
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| Preface |
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vi | |
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1 | (52) |
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2 | (12) |
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2 | (3) |
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5 | (5) |
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Computation of approximants |
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10 | (1) |
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Approximating the value of K(an/bn) |
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11 | (3) |
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Regular continued fractions |
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14 | (11) |
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14 | (3) |
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Best rational approximation |
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17 | (4) |
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Solving linear diophantine equations |
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21 | (1) |
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22 | (1) |
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23 | (2) |
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Rational approximation to functions |
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25 | (5) |
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25 | (2) |
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27 | (3) |
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Correspondence between power series and continued fractions |
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30 | (8) |
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From power series to continued fractions |
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30 | (3) |
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From continued fractions to power series |
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33 | (1) |
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One fractio, two series; analytic continuation |
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33 | (2) |
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35 | (3) |
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More examples of applications |
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38 | (8) |
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38 | (1) |
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Moment problems and divergent series |
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39 | (3) |
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42 | (1) |
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43 | (2) |
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45 | (1) |
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46 | (2) |
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48 | (5) |
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53 | (46) |
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54 | (23) |
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Properties of linear fractional transformations |
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54 | (5) |
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Convergence of continued fractions |
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59 | (1) |
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60 | (3) |
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63 | (2) |
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Tail sequences and three term recurrence relations |
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65 | (5) |
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70 | (3) |
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73 | (4) |
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Transformations of continued fractions |
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77 | (12) |
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77 | (1) |
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Equivalence transformations |
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77 | (5) |
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The Bauer-Muir transformation |
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82 | (3) |
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Contractions and extensions |
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85 | (2) |
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Contractions and convergence |
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87 | (2) |
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89 | (2) |
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91 | (8) |
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99 | (72) |
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100 | (16) |
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The Stern-Stolz Divergence Theorem |
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100 | (3) |
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The Lane-Wall Characterization |
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103 | (3) |
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106 | (2) |
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Mapping with linear fractional transformations |
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108 | (6) |
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The Stieltjes-Vitali Theorem |
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114 | (1) |
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115 | (1) |
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Classical convergence theorems |
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116 | (44) |
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Positive continued fractions |
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116 | (6) |
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Alternating continued fractions |
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122 | (2) |
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Stieltjes continued fractions |
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124 | (5) |
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The Sleszynski-Pringsheim Theorem |
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129 | (6) |
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135 | (7) |
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142 | (6) |
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148 | (3) |
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151 | (9) |
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Additional convergence theorems |
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160 | (5) |
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Simple bounded circular value sets |
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160 | (3) |
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Simple unbounded circular value sets |
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163 | (2) |
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165 | (1) |
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166 | (5) |
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Periodic and limit periodic continud fractions |
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171 | (46) |
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Periodic continued fractions |
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172 | (14) |
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172 | (1) |
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Iterations of linear fractional transformations |
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172 | (2) |
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Classification of linear fractional tranformations |
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174 | (2) |
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General convergence of periodic continued fractions |
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176 | (3) |
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Convergence in the classical sense |
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179 | (2) |
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Approximants on closed form |
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181 | (2) |
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A connection to the Parabola Theorem |
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183 | (3) |
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Limit periodic continued fractions |
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186 | (17) |
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186 | (1) |
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Finite limits, loxodromic case |
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187 | (5) |
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Finite limits, parabolic case |
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192 | (4) |
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Finite limits, elliptic case |
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196 | (4) |
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200 | (3) |
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Continued fractions with multiple limits |
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203 | (2) |
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Periodic continued fractions with multiple limits |
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203 | (1) |
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Limit periodic continued fractions with multiple limits |
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204 | (1) |
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205 | (6) |
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205 | (1) |
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205 | (2) |
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Fixed circles and periodic continued fractions |
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207 | (4) |
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211 | (1) |
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212 | (5) |
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Numerical computation of continued fractions |
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217 | (48) |
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218 | (20) |
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218 | (1) |
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219 | (4) |
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auxiliary continued fractions |
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223 | (4) |
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The improvement machine for the loxodromic case |
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227 | (5) |
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Asymptotic expansion of tail values |
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232 | (3) |
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The square root modification |
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235 | (3) |
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238 | (22) |
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238 | (2) |
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240 | (3) |
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The Oval Sequence Theorem |
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243 | (1) |
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An algorithm to find value sets for a given continued fractions of form K (an/1) |
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244 | (4) |
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Value sets and the fixed point method |
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248 | (7) |
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Value sets B(wnPn) for limit 1-periodic continued fractions of loxodromic or parabolic type |
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255 | (3) |
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Error bounds based on idea 3 |
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258 | (2) |
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Stable computation of approximants |
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260 | (1) |
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Stability of the backward recurrence algorithm |
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260 | (1) |
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261 | (1) |
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262 | (3) |
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Some continued fraction expansions |
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265 | (30) |
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265 | (1) |
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265 | (1) |
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266 | (1) |
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266 | (9) |
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266 | (2) |
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268 | (1) |
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The general binomial function |
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269 | (1) |
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270 | (2) |
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Trigonometric and hyperbolic functions |
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272 | (1) |
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Inverse trigonometric and hyperbolic functions |
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273 | (1) |
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Continued fractions with simple values |
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274 | (1) |
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275 | (16) |
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275 | (2) |
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Special examples with oF1 |
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277 | (1) |
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Special examples with 2F0 |
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277 | (4) |
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Special examples with 1F1 |
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281 | (1) |
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Special examples with 2F1 |
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281 | (1) |
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282 | (2) |
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Gamma function expressions |
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284 | (7) |
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Basic hypergeometric functions |
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291 | (4) |
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291 | (1) |
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292 | (1) |
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292 | (3) |
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| Bibliography |
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295 | (11) |
| Index |
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306 | |
