| Preface | p. xi |
| Notation | p. xiii |
| General considerations | p. 1 |
| Part one | p. 1 |
| Part two | p. 2 |
| Part three | p. 2 |
| Basic Theory | |
| Basics | p. 9 |
| Symbols and notation | p. 9 |
| Definitions | p. 10 |
| Recurrence relations | p. 13 |
| Equivalence transformations | p. 15 |
| Contractions and extensions | p. 16 |
| Continued fractions with prescribed approximants | p. 18 |
| Connection between continued fractions and series | p. 19 |
| Periodic and limit periodic continued fractions | p. 21 |
| Tails of continued fractions | p. 23 |
| Continued fractions over normed fields | p. 26 |
| Generalisations of continued fractions | p. 28 |
| Continued fraction representation of functions | p. 29 |
| Symbols and notation | p. 29 |
| Correspondence | p. 30 |
| Families of continued fractions | p. 35 |
| Correspondence of C-fractions | p. 39 |
| Correspondence of P-fractions | p. 40 |
| Correspondence of J-fractions and T-fractions | p. 41 |
| Correspondence and three-term recurrences | p. 42 |
| Convergence criteria | p. 45 |
| Some classical theorems | p. 45 |
| Convergence sets and value sets | p. 47 |
| Parabola and oval theorems | p. 49 |
| Correspondence and uniform convergence | p. 52 |
| Periodic and limit periodic continued fractions | p. 53 |
| Convergence and minimal solutions | p. 56 |
| Pade approximants | p. 59 |
| Definition and notation | p. 59 |
| Fundamental properties | p. 60 |
| Connection with regular C-fractions | p. 64 |
| Connection with P-fractions | p. 65 |
| Extension of the Pade table | p. 67 |
| Connection with M-fractions and the M-table | p. 68 |
| Convergence of Pade approximants | p. 70 |
| Formal orthogonality property | p. 72 |
| Moment theory and orthogonal functions | p. 77 |
| Moment theory | p. 77 |
| Stieltjes transforms | p. 85 |
| Construction of solutions | p. 90 |
| Orthogonal polynomials | p. 91 |
| Monic orthogonal polynomials on R and J-fractions | p. 92 |
| Szego polynomials and PPC-fractions | p. 100 |
| Orthogonal Laurent polynomials and APT-fractions | p. 102 |
| Numerics | |
| Continued fraction construction | p. 107 |
| Regular C-fractions | p. 107 |
| C-fractions | p. 113 |
| S-fractions | p. 114 |
| P-fractions | p. 11 |
| J-fractions | p. 120 |
| M-fractions | p. 122 |
| Positive T-fractions | p. 124 |
| Thiele fractions | p. 125 |
| Truncation error bounds | p. 129 |
| Parabola theorems | p. 129 |
| The oval sequence theorem | p. 131 |
| The interval sequence theorem | p. 136 |
| Specific a priori bounds for S-fractions | p. 138 |
| A posteriori truncation error bounds | p. 140 |
| Tails and truncation error bounds | p. 143 |
| Choice of modification | p. 143 |
| Continued fraction evaluation | p. 149 |
| The effect of finite precision arithmetic | p. 149 |
| Evaluation of approximants | p. 152 |
| The forward recurrence and minimal solutions | p. 154 |
| Round-off error in the backward recurrence | p. 156 |
| Special Functions | |
| On tables and graphs | p. 163 |
| Introduction | p. 163 |
| Comparative tables | p. 163 |
| Reliable graphs | p. 168 |
| Mathematical constants | p. 175 |
| Regular continued fractions | p. 175 |
| Archimedes' constant, symbol [pi] | p. 176 |
| Euler's number, base of the natural logarithm | p. 178 |
| Integer powers and roots of [pi] and e | p. 180 |
| The natural logarithm, ln(2) | p. 181 |
| Pythagoras' constant, the square root of two | p. 183 |
| The cube root of two | p. 183 |
| Euler's constant, symbol [gamma] | p. 185 |
| Golden ratio, symbol [phi] | p. 185 |
| The rabbit constant, symbol [rho] | p. 186 |
| Apery's constant, [zeta](3) | p. 188 |
| Catalan's constant, symbol C | p. 189 |
| Gompertz' constant, symbol G | p. 190 |
| Khinchin's constant, symbol K | p. 190 |
| Elementary functions | p. 193 |
| The exponential function | p. 193 |
| The natural logarithm | p. 196 |
| Trigonometric functions | p. 200 |
| Inverse trigonometric functions | p. 204 |
| Hyperbolic functions | p. 210 |
| Inverse hyperbolic functions | p. 213 |
| The power function | p. 217 |
| Gamma function and related functions | p. 221 |
| Gamma function | p. 221 |
| Binet function | p. 224 |
| Polygamma functions | p. 229 |
| Trigamma function | p. 232 |
| Tetragamma function | p. 235 |
| Incomplete gamma functions | p. 238 |
| Error function and related integrals | p. 253 |
| Error function and Dawson's integral | p. 253 |
| Complementary and complex error function | p. 261 |
| Repeated integrals | p. 268 |
| Fresnel integrals | p. 269 |
| Exponential integrals and related functions | p. 275 |
| Exponential integrals | p. 275 |
| Related functions | p. 285 |
| Hypergeometric functions | p. 291 |
| Definition and basic properties | p. 291 |
| Stieltjes transform | p. 295 |
| Continued fraction representations | p. 295 |
| Pade approximants | p. 309 |
| Monotonicity properties | p. 313 |
| Hypergeometric series [subscript p]F[subscript q] | p. 315 |
| Confluent hypergeometric functions | p. 319 |
| Kummer functions | p. 319 |
| Confluent hypergeometric series [subscript 2]F[subscript 0] | p. 330 |
| Confluent hypergeometric limit function | p. 333 |
| Whittaker functions | p. 334 |
| Parabolic cylinder functions | p. 337 |
| Bessel functions | p. 343 |
| Bessel functions | p. 343 |
| Modified Bessel functions | p. 356 |
| Probability functions | p. 371 |
| Definitions and elementary properties | p. 371 |
| Normal and log-normal distributions | p. 373 |
| Repeated integrals | p. 377 |
| Gamma and chi-square distribution | p. 378 |
| Beta, F- and Student's t-distributions | p. 382 |
| Basic hypergeometric functions | p. 391 |
| Definition and basic properties | p. 391 |
| Continued fraction representations | p. 395 |
| Higher order basic hypergeometric functions | p. 399 |
| Bibliography | p. 401 |
| Index | p. 421 |
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