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Lightstone A.H., Robinson A. — Nonarchimedean Fields and Asymptotic Expansions
Lightstone A.H., Robinson A. — Nonarchimedean Fields and Asymptotic Expansions

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Название: Nonarchimedean Fields and Asymptotic Expansions

Авторы: Lightstone A.H., Robinson A.

Язык: en

Рубрика: Математика/Анализ/Продвинутый анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1975

Количество страниц: 204

Добавлена в каталог: 02.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$m_0$      77
$m_1$      77
Absolute convergence      196
Absolute value      12
Archimedean property      7 9
Archimedean valuation      17
Archimedes      61
Asymptotic expansions      139 195
Asymptotic power series      144
Asymptotic sequences      138
Asymptotic series      141
Asymptotically equal functions      172
Asymptotically finite function      172
Atomic statement      41
Bellman, Richard      118
Bernoulli numbers      124
Bernoulli polynomials      124
Bolzano      61
Bourbaki, n      30
Cauchy product      25
Cauchy sequence      1 85
Cofinite subset      43
Compactness Theorem      36
Comparable sequences      167
Complete field      20
Completeness theorem      35
Constant function      29
Continuity      62
Continuity $m^{\rho}r$      107
Continuity at a standard number      61
Continuity, monadic      69
Continuity, q-      68 113
Continuity, s-      70 110
Continuity, sequential      107
Continuity, uniform      63
Convergence      20
Convergence in $\mathcal{P}$      175
Convergent sequence      19
Convergent Series      22
Copson, E.T.      151
Criterion for asymptotic expansions      141 154 156 171
Criterion for asymptotically finite functions      174
Criterion for convergence in $\mathcal{P}$      183
Criterion for convergence of series in $\mathcal{P}$      193
Criterion for equivalent functions      159
Criterion for iotas      94
Derivative      74
Derivative in $^{\rho}\mathcal{r}$      117
Diagonal relation      5
Dirac delta function      67 105
Dirac delta function, derivative      75 105
Elementary extension      49
Empty set requirement      43
Equality      4
Equivalence relation      4
Erdelyi, A.      195
Euclid      61
Eudoxus      61
Euler — maclaurin, approximation      129 130
Euler — maclaurin, expansion      129
Euler — maclaurin, formula      125 128
Euler — maclaurin, quadrature formula      123 124
Euler’s constant      131
Exponential integral function      118
EXTERNAL      39
External function      40
External language      42
External sequence      40
External statements      42
External subset      40
Field      8
Field, $\mathcal{L}$      31
Field, $\mathcal{R}$      35
Field, Archimedean      10
Field, complete      20
Field, hardy      29
Field, nonarchimedean      10
Field, ordered      9
Field, residue class      13 17
Fifth principle of permanence      97
Filter      43
Filter, empty set requirement      43
Filter, fixed      43
Filter, free      43
Filter, intersection requirement      43
Filter, maximal      45
Filter, superset requirement      43
Filter, ultrafilter requirement      44
Finite closed interval      63
Finite number      12
First principle of permanence      56
Fourth principle of permanence      97
Function      48
Function in a field      100
Function, asymptotically equal      172
Function, asymptotically finite      172
Function, constant      29
Function, continuous      61 62
Function, derivative      74
Function, Dirac delta      67 75
Function, exponential integral      118
Function, identity      12
Function, incomplete factorial      118
Function, polynomial      11
Function, standard      100
Fundamental theorem about finite numbers      39
Group of units      17
Group, abelian      5
Group, archimedean      5 8
Group, nonarchimedean      8
Group, ordered      7
Group, valuation      17
Hardy fields      29
Ideal      76
Ideal, maximal      76
Ideal, proper      76
Ideal, valuation      17
Identity relation      5
Incomplete factorial function      118
Infinite number      12
Infinite number, large      94
Infinitesimal      12
Infinitesimal, small      94
infinity      14
Internal      39
Internal function      40
Internal language      42
Internal sequence      40
Internal statement      42
Internal subset      40
Intersection requirement      43
Iota      94
Jeffreys, harold and jeffreys, b.s.      118 121 125
Language, external      42
Language, internal      42
Laugwitz, d., v.      31
Laurent series      15
Levi-Civita, T.      v 31
Lightsone, a.h.      39 120
Limit of convergent sequence      19 64
Lipschitz condition      102
Los’s lemma      49
Los’s lemma, proof      50—53
Many-sorted calculus      1
Many-sorted structures      1
Many-sorted structures, language      1
Maximal      45
Maximal filter      45
Maximal ideal      76
Mega      94
Metric      18
Metric space      19
Monad      13
Monadic continuity      69
Nonarchimedean field      10
Nonarchimedean group      8
Nonarchimedean valuation      14 18
Nonstandard criterion for asymptotic expansions      156
Nonstandard criterion for convergence in $\mathcal{P}$      183
Norm      180
Norm on $\mathcal{P}$      180 187
Number, bernoulli      124
Number, finite      12
Number, infinite      12
Number, infinitesimal      12
Number, natural      48
Number, real      48
Number, standard part      39
One-sorted system      3
Ordered group      7
Ordered set      6
Ostrowski, A.      v 31
P-series      90
Peano’s induction postulate for $\mathcal{R}$      40
Peano’s induction postulate for $^{\ast}\mathcal{r}$      56
Poincare, H.      137
Polynomial Bernoulli      124
Polynomial degree      11
Polynomial function      11
Popken, J.      172 187
Principle of mathematical induction for $\mathcal{R}$      40
Principle of mathematical induction for $^{\ast}\mathcal{r}$      58
Principle of permanence      56
Principle of permanence, fifth      97
Principle of permanence, first      56
Principle of permanence, fourth      97
Principle of permanence, second      57
Principle of permanence, sixth      98
Principle of permanence, third      57
Proper ideal      76
Q-continuity      68 113
Relation, diagonal      5
Relation, equality      4
Relation, equivalence      4
Relation, identity      5
Relation, irreflexive      6
Relation, substitutive      4
Relation, total      6
Relation, transitive      6
Residue class field      13 17
Ring of cosets      77
Ring, valuation      17
Robinson, Abraham      30 39 53 79
S-continuity      70 110
Second principle of permanence      57
Seq-continuity      107
SEQUENCE      19 48
Sequence, asymptotic      138
Sequence, comparable      167
Sequence, convergent      19 175
Sequence, gauchy      1 85
Sequence, limit      19 64
Sequence, sum      25
Sequentially comprehensive      55
Sequentially continuous      107
Series, $\rho-$      90
Series, asymptotic      141
Series, asymptotic power      144
Series, cauchy product      25
Series, convergent      22
Series, Laurent      15
Series, sum      64
Set, basic      3
Set, ordered      6
Set, supporting      2
sgn      126
Sixth principle of permanence      98
Standard map      48
Standard object      48
Standard part      39
Statement      41
Statement, atomic      41
Statement, external      42
Statement, false      42
Statement, internal      42
Statement, length      50
Statement, true      42
Stirring’s formula      136
Stokes’ phenomenon      151
Subset      48
Subset, cofinite      43
Substitutive relation      4
Superset requirement      43
Supporting set      2
Third principle of permanence      57
Transfer theorem      37
Triangle inequality      12 18
Trichotomy Law      6
Ultrafilter requirement      44
Ultrametric inequality      19
Ultrapower theorem      49
Uniform continuity      63
Valuation, archimedean      17
Valuation, group      17
Valuation, ideal      17
Valuation, nonarchimedean      14 18
Valuation, p-adic      15
Valuation, ring      17
Valuation, trivial      15
van der Corput, J.G.      137 172 195
VS      48
Watson’s lemma      162
Weierstrass      61
Zorn’s Lemma      45
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