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Rockett A.M., Szusz P. — Continued Fractions
Rockett A.M., Szusz P. — Continued Fractions



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Название: Continued Fractions

Авторы: Rockett A.M., Szusz P.

Язык: en

Рубрика: Математика/Анализ/Непрерывные дроби/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 188

Добавлена в каталог: 01.12.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adams, William W.      36
Approximation by intermediate convergents      112
Approximation by non-convergents      112
Approximation, asymmetric      110
Approximation, homogeneous      19
Approximation, inhomogeneous      116 136
Auxiliary convergent      36
Babenko, K. L      166
Barnes, E. S.      136
Beppo Levi Theorem      141
Bernstein, Felix      169
Best approximation      17 19
Best approximation, arc sine law      167
Best approximation, first kind      36
Best approximation, second kind      36
Billingsley, Patrick      viii 167
Borel sets      137
Borel — Cantelli lemma      140
Borel, Emile      135
Brillhart, John      135
Brouncker, William      64
Calendar construction      60 134
Cantor set      72
Cantor set, sum      73
Cantor set, sum, direct construction      135
Cassels, J. W. S.      17 136
Cattle problem of Archimedes      134
Central limit theorem      167
Ceulen, Johannes van      134
Characteristic equation      58
Charves, M.      41
Chebyshev’s inequality      145
Chinese remainder theorem      51
Conjugate of a quadratic surd      43
Continued fraction      1
Continued fraction with bounded digits      72 74
Continued fraction, complete quotient      4
Continued fraction, complex partial quotient      17
Continued fraction, convergent      1
Continued fraction, convergent, of a reciprocal      10
Continued fraction, general      58
Continued fraction, partial quotient      1
Continued fraction, regular      3
Continued fraction, to the nearest integer      18
Continued fraction, transformation      8
Convergent      1
Convergent, auxiliary      36
Convergent, denominator      2
Convergent, intermediate      36
Convergent, numerator      2
Convergent, principal      36
Convergent, quasi-      36
Cousins, Frank W.      134
Cusick, Thomas W.      135 136
Davenport, Harold      37 135 136
Descombes, Roger      37 136
Dickson, Leonard Eugene      17 18 134 135 136
Difference      9
Diophantine approximation      19
Diophantine approximation, homogeneous      19
Diophantine approximation, inhomogeneous      116 136
Diophantine approximation, metrical      169
Durner, Alexander      viii
Dutka, Jacques      134
e      13
e approximation      30
e approximation by convergents      37
e approximation by non-convergents      115
e linear recurrence (example)      53
Equivalent, quadratic forms      84
Equivalent, real numbers      6
Erdos, Paul      175
Ergodic theorem      167
Euclidean algorithm      17
Euler, Leonhard      18 40 51 64 66 69
Event      137
Event, probability      137
Event, probability one      138
Event, probability zero      137
Farey sequence      134 136
Fermat, equation      134
Fermat, Pierre de      64
Fermat, sum of two squares      69
Fibonacci sequence      12 54
Fibonacci sequence, Ostrowski representation      24
Flahive, Mary E.      135 136
Forder, H. G.      135
Fraenkel, Aviezri S.      36
Freiman, G. A.      136
G      11 39
g approximation by by non-convergents      113
g approximation by convergents      80—81
g approximation by inhomogeneous      122 130
Galois, Evariste      45
Gauss — Kuzmin theorem      151
Gauss, K. F.      135 151 166
Gear ratio problem      59
Gear ratio problem, general      64
Girard, Albert      69
Goldbach, Christian      64
Golden ratio      11 18 39
Grace, J. H.      36
h, conjugate of g      12
Halberstam, Heini      134
Hall, Jr., Marshall      78 135
Hall, ray      136
Hall, theorem      72
Hardy, G. H.      vii 17 58 136
Hermite, Charles      69 71 135
Hickerson, Dean R.      58
Homogeneous problem      19
Hua, Loo-keng      134
Hurwitz, Adolph      vii 17 80 135
Huygens, Christiaan      59 134
Inhomogeneous approximation      32 37 116
Inhomogeneous approximation, Khintchine      122
Inhomogeneous approximation, Minkowski      117
Intermediate convergent      36
Interval of order n      138
Inverse period      46
Ito, Shunji      18
Jacobsthal, E.      135
Jones, William B.      vii 17
Jurev, S. P.      166
Kac, Mark      viii
Khintchine — Levy constant      164
Khintchine — Levy, theorem      163
Khintchine, A. Ya.      vii 17 36 122 136 146 160 163 167 170
Khintchine, constant      163
Khintchine, theorem      160
Koksma, J. F.      136
Kolmogorov-type inequality      150 174
Kuzmin, R. O.      152
Lagrange, chain of forms      92
Lagrange, Joseph-Louis      22 41 50 134
Lagrange, spectrum      84
Lagrange, spectrum, alternative definition      93
Landau order notation      ix
Lang, Serge      36
Laplace, Pierre-Simon      151 166
Lattice point      131
Law of iterated logarithm      167
Law of Large Numbers      145
Law of Large Numbers, strong      148
Law of large numbers, strong, with error term      149
Law of large numbers, weak      146
Lebesgue dominated convergence theorem      141
Lebesgue measure      137
Lebesgue — Stieltjes integral      143
Legendre, Adrien-Marie      22 36 46 69 135
Lekkerkerker, C. K.      36
LeVeque, William J.      vii 17 36 58 134 135 136 175 176
Levy, Paul      viii 18 152 156 163 167
Linear recurrence      53 58
Mahler, K.      136
Markov, A. A.      146
Markov, chain      104 105
Markov, form      103
Markov, number      101
Markov, spectrum      85
Markov, spectrum, alternative definition      93
Markov, triple      101
Markov, triple, complete      103
Markov, triple, neighbors      102
Markov, triple, non-singular      101
Markov, triple, singular      101
Markowsky, George      18
Mathews, Jerold      134
Minkowski, Hermann      117 131
Modular group      17
Mordell, Louis Joel      131
Niven, Ivan, vii, viii      17 58 135
Ostrowski, Alexander      24 36
Ostrowski, algorithm      24
Ostrowski, representation      24 36 37
Ostrowski, representation negative integer      32
Ostrowski, representation using Fibonacci numbers      24
Ostrowski, representation using g      24 36
Partial quotient      1
Partial quotient, arithmetic mean      142
Partial quotient, bounded      138
Partial quotient, geometric mean      163
Partial quotient, real valued      111
Partial quotient, relative frequency      162
Partial quotient, weakly dependent      159
Pell, John      64 134
Pell’s equation      vii 31 64 69
Periodic continued fraction      39
Periodic continued fraction, examples      44—45 47—49
Periodic continued fraction, initial block      39
Periodic continued fraction, inverse period      46
Periodic continued fraction, period      39
Periodic continued fraction, period length      49
Periodic continued fraction, purely      39
Periodic continued fraction, repeating block      39
Perron, Oskar      vii 17 18 36 58 135
Philipp, Walter      viii 167 176
Piper’s algorithm      134
Planetarium      59
Podsypanin, E. V.      58
Principal convergent      36
Quadratic form, (real, indefinite binary)      84
Quadratic form, chain      89
Quadratic form, discriminant      84
Quadratic form, equivalent      84
Quadratic form, inverse equivalence      91
Quadratic form, minima      18 84
Quadratic form, neighbor      88
Quadratic form, properly represented number      86
Quadratic form, reduced      86
Quadratic form, roots      84
Quadratic residue      51
Quadratic surd      39
Quadratic surd, conjugate      43
Quadratic surd, discriminant      39
Quadratic surd, reduced      45
Quasi-convergent      36
Rademacher, Hans      17
Random variable      141
Random variable, density function      143
Random variable, distribution function      143
Random variable, expectation      141
Random variable, joint distribution function      144
Random variable, mixing sequence      167
Random variable, mutually independent      166
Random variable, n-th moment      143
Random variable, pairwise independent      144
Random variable, totally independent      144
Random variable, variance      144
Random variable, weakly dependent      144
Remak, Robert      136
Renyi, Alfred      viii 166
Revesz, Pal      viii 166
Rieger, Georg Johann      18
Rockett, Andrew M.      18 37 135
Ryll-Nardzewski, Czeslaw      viii 167
Schmidt, Wolfgang M.      175 176
Segre, Beniamino      110
Series, Caroline      136 167
Serre, Jean-Pierre      17
Serret, J. A.      135
Set, $\sigma$-algebra      137
Set, almost everywhere      138
Set, Borel      137
Set, complement      137
Set, measure zero      137
Set, pairwise disjoint      137
Shanks, Daniel      135
Simson, Robert      18
Sos, Vera T.      37
Sprindzuk, Vladimir G.      176
Stout, William      167
Swinnerton-Dyer, H. P. F.      136
Szekeres, George      130 136
Szusz, Peter      37 135 136 166 176
t-expansion      32 116 136
Tanaka, Shigeru      18
Ternary notation      72
Thron, Wolfgang J.      vii 17
Truncation      146
Unimodular, relation between t and $\zeta_{k+1}$      6 41
Unimodular, transformation      6
Uspensky, J. V.      166
Vahlen, K. Th.      135
Volkmann, Bodo      viii
Wall, H. S.      vii 17
Wallis, John      64
Waterman, Michael S.      166
Weil, Andre      viii 134 136
Wirsing , Eduard      166
Wolffing, E.      viii
Wright, E. M.      vii 17 58 135 136
Zuckerman, H. S.      vii 17 58 135
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