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Knopp K., Bagemihl F. — Infinite Sequences and Series
Knopp K., Bagemihl F. — Infinite Sequences and Series

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Название: Infinite Sequences and Series

Авторы: Knopp K., Bagemihl F.

Аннотация:

Careful presentation of fundamentals of the theory by one of the finest modern expositors of higher mathematics. Covers functions of real and complex variables, arbitrary and null sequences, convergence and divergence, Cauchy's limit theorem, more.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1956

Количество страниц: 186

Добавлена в каталог: 15.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\overline{fin}$      14
$\overline{lim}$      16 27
$\overline{\underline{lim}}$      34
$\pi$, calculation of      165
$\underline{lim}$      16 27
$\varepsilon$-neighborhood      12
Abel, N.H.      63 66 125 137
Abel’s limit theorem      109 145 169
Abel’s partial summation      70 130
Abel’s Test      136 137
Absolute convergence      70
Absolute value      10
Absolutely convergent product      96
Absolutely convergent sequence      72
Absolutely convergent series      71
Adams, J.C.      167
Addition of convergent series      78
Addition theorem      92 152 153
Agnew, R.P.      132
Alterations, theorem on finitely many      50
Alternating series      68
Amplitude      10
Amplitude, principal value of      10
Analytic function      102
Approach a limit      29
Approach, radial      109
Approximation      1 29
Arbitrary sequences      18
Arbitrary sequences, test for      43
Arbitrary terms, series of      67
Argument      10
Arrangement by diagonals      28 90
Arrangement by squares      28 90
Associative law      5 75
Asymptotically equal      31
Asymptotically proportional      30
Axis, imaginary      10
Axis, number      5
Axis, real      10
Base of natural logarithms      54
Behavior, convergence      62
Bernoullian numbers      118 119 174
Best possible theorem      142
Better convergence      128
Binomial expansion      4
Binomial expansion, extension of      109 151
Binomial series      140 158 159
Binomial theorem      109 151
Bisection method      39
Bolzano — Weierstrass theorem      15 42
Bound      13
Bound, lower      14
Bound, lower, greatest      14 26
Bound, upper      14
Bound, upper, least      14 26
Boundary      12
Boundary of circle of convergence      100 109
Boundary point of a set      13
Bounded from above      14
Bounded from below      14
Bounded on the left      14 19
Bounded on the right      14 19
Bounded sequence      19
Bounded set      13
Bounded variation      72
Boundedly divergent sequence      30
Bounds, oscillation between finite      47
Bounds, oscillation between infinite      47
Briggsian logarithms      167
Bromwich, T.J.I’A.      169 175
C      41 65
Calculating machine      165 166
Calculation, numerical      164
Calculation, numerical, of $\pi$      165
Calculation, numerical, of e      165
Calculation, numerical, of natural logarithms      166
Calculation, numerical, of roots      167
Calculation, numerical, of trigonometric functions      168
Calculus, differential      17 35
Cauchy product of series      90 145
Cauchy — Hadamard formula      100 113
Cauchy — Toeplitz theorem      73
Cauchy, A.L.      42 57 58
Cauchy, theorem of      90
Cauchy’s condensation test      62
Cauchy’s double-series theorem      172
Cauchy’s limit theorem      33 37 110 144
Cauchy’s limit theorem, generalizations of      34
Center, transformation to a new      105
Cesaro, E.      126
Circle of convergence      99 100
Circle of convergence, boundary of      100 109
Circle, unit      99
Circular functions      150 152
Closed evaluation of series      163 168
Closed interval      13
Closed set      13
Coefficients, comparison of      105
Coefficients, undetermined      117
Column series      84
Column sum      106
Column-condition      35
Common logarithms      167
Common logarithms, modulus of      167
Commutative law      5 75 79
Comparison of coefficients      105
Comparison test of the first kind      56
Comparison test of the second kind      57 132
Comparison tests      52 55 56 57 132
Comparison tests in the extended sense      137
Complement      13
Completeness theorem for the real number system      7
Complex domain      10
Complex number, finite      26
complex numbers      9
Complex numbers, polar form of      10
Complex numbers, trigonometric representation of      10
Complex plane      10
Complex point set      19
Complex sequence      18
Complex variable      16
Composite function      112
Composite functions, expansion of      110 112
Condensation test      62
Condition, column-      35
Condition, norm-      35
Condition, row-.      35
Conditionally convergent      82
Constant, Euler’s      65
Continuity      17
Continuity of functions represented by power series      102 107
Continuity, theorem of      7
Convergence behavior      62
Convergence tests for sequences      38 43
Convergence tests, scales of      128
Convergence, absolute      70
Convergence, better      128
Convergence, circle of      99 100
Convergence, faster      128
Convergence, radius of      100
Convergence, slower      128
Convergence, worse      128
Convergence-preserving transformation      74
Convergent majorant      77
Convergent product      93
Convergent product, nonabsolutely      98
Convergent sequence      29
Convergent Series      44
Convergent series, addition of      78
Convergent series, everywhere      59 99
Convergent series, multiplication of      89 145
Convergent series, operating with      74
Convergent series, subtraction of      78
Convergent, absolutely      71 96
Convergent, conditionally      82
Convergent, everywhere      59 99
Convergent, nonabsolutely      71 98
Convergent, unconditionally      81
Cramer’s Rule      117
Cut, Dedekind      6
Cut-number      7
Cyclometric functions      160
Decimal fraction      60 164
Decomposition of a sequence      22
Decomposition, partial-fractions      155 156
Decreasing function      11
Decreasing sequence      11 19
Decreasing sequence, monotonically      19
Decreasing sequence, strictly      19
Dedekind cut      6
Dedekind, fundamental theorem of      7
Dedekind, R.      137
Definite integral      109
Definitely divergent sequence      30
Definitely divergent series      45
Definition, domain of      17
Dense      5
Derived rules      11
Development of a function in a power series      102
Diagonals, arrangement by      28 90
Differentiability      17
Differentiability of functions represented by power series      107
Differential calculus      17 35
digit      60
Dilution of series      51 82
Dini, U.      125 127
Dirichle series      138
Dirichle, G. L.      137
Dirkhlet’s test      136 137
Distance      11
Distributive law      5 75 78 88
Divergence tests, scales of      129
Divergence, faster      128
Divergence, slower      128
Divergence, strength of      66
Divergence, stronger      128
Divergence, weaker      128
Divergent product      97
Divergent sequence      30
Divergent sequence, boundedly      30
Divergent sequence, definitely      30
Divergent sequence, indefinitely      30
Divergent sequence, unboundedly      30
Divergent series      45
Divergent series, definitely      45
Divergent series, indefinitely      45
Divergent series, summation of      145
Doerrie, H.      175
Domain of definition      17
Domain of values      17 154 155
Domain, complex      10
Domain, real      11
Double sequence      28
Double series      86
Double-series theorem, Cauchy’s      172
e      40 54
e, calculation of      165
Element of a set      12 26
Elementary functions      3 17 149
Elementary functions, expansion of      149
Empty set      12
Entire function      152
Entire plane      99
Enumerable set      27
Equal, asymptotically      31
Equation, functional      92
Equation, quadratic      8
Error      29 50 164
Error, estimate of      61 66
Estimate of error      61 66
Estimation of remainder      164 165
Euler, L.      9
Eulerian numbers      119
Euler’s constant      65
Euler’s transformation      144 171
Evaluation of series, closed      163 168
Evaluation of series, numerical      163 165
Even function      105
Everywhere convergent      59 99
Expansion of a function in a power series      102
Expansion of a reciprocal      115
Expansion of composite functions      110 112
Expansion of elementary functions      149
Expansion, binomial      4
Expansion, Maclaurin      108
Expansion, Taylor      108
Exponential function      92 150 152
Exponential function, general      151
Extended rearrangement theorem      84
Extension of the binomial theorem      109
Extension of the rational number system      7
Faber, G.      175
Fabry, E.      169 175
Factor of a product      93 94
Factor series      90
Faster convergence      128
Faster divergence      128
Field      5
Field of real numbers      7
Field, ordered      5
FIN      14 26
Fin inf      14
Fin sup      14
Finis inferior      14
Finis superior      14
Finite complex number      26
Finitely many alterations, theorem on      50
First main test for sequences      38
First main test for sequences for series      52
Formula, Cauchy — Hadamard      100 113
Formula, recursion      117
Formulas for Abel’s partial summation      130
Formulas for integration by parts      130
Fort, T.      175
FRACTION      4
Fraction, decimal      60 164
Fraction, partial      151
Fraction, proper      58
Function of a complex variable      16
Function of a real variable      16
Function theory      17
Function, analytic      102
Function, circular      150 152
Function, composite      110 112
Function, cyclometric      160
Function, decreasing      11
Function, elementary      3 17 149
Function, entire      152
Function, even      105
Function, exponential      92 150 152
Function, exponential, general      151
Function, hyperbolic      150
Function, increasing      11
Function, inverse      120 150
Function, inverse trigonometric      160
Function, logarithmic      156
Function, multiple-valued      158
Function, odd      105
Function, rational      150 151
Function, reciprocal      115
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