|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Knopp K., Bagemihl F. — Infinite Sequences and Series |
|
|
|
| Предметный указатель |
 14
 16 27
 34
 , calculation of 165
 16 27
 -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 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
|
|
|
| Реклама |
|
|
|
|
|
О проекте