|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Knopp K., Bagemihl F. — Infinite Sequences and Series |
|
|
|
| Предметный указатель |
Function, regular 102
Function, trigonometric 150 152
Functional equation 92
Functions represented by power series 102
Functions represented by power series, continuity of 102 107
Functions represented by power series, differentiability of 107
Functions, development of 102
Functions, expansion of 102 149
Functions, representation of 102
Fundamental laws of order 5
Fundamental operations 5
Fundamental rules of operation 75
Fundamental theorem of Dedekind 7
g.l.b. 14 26
Gauss, C.F. 136
General exponential function 151
General power 150 158
Geometric series 54 72
Goniometry 153
Greatest lower bound 14 26
Hadamard — Cauchy formula 100 113
Hardy, G.H. 146
Harmonic series 47
Harmonic series with exponent  54
Hyperbolic functions 150
Hyslop, J.M. 175
i 8 9
Identity theorem for power series 103
Imaginary axis 10
Imaginary part 10
Improper limit 30
Increasing function 11
Increasing sequence 11 19
Increasing sequence, monotonically 19
Increasing sequence, strictly 19
Indefinitely divergent sequence 30
Indefinitely divergent series 45
Index of a term of a sequence 1
Index of summation 4
Inequalities 12
inf 14
Infinite matrix 28
Infinite product 4 48 92
Infinite sequence 1 i6
Infinite series 2 44
Infinite series, operating with 45
Infinite set 12
infinity 26
Infinity, point at 26
Insertion of parentheses 45 75
INTEGER 4
Integer, negative 4
Integral test 64
Integral, definite 109
Integral, partial 64
Integration by parts 130
Interchange of order of summation 87
Interior point of a set 13
interval 13
Interval, closed 13
Interval, open 13
Interval, semiopen 13
Intervals, principle of nested 39
Invariably 19
Inverse function 120 150
Inverse trigonometric function 160
Inversion of power series 119
Irrational number 7
Isolated point of a set 13
Isomorphic 9
Iterated series 86
Jehle, H. 132
Knopp, K. 87 169 175 176
Kummer, E.E. 87
Kummer’s transformation 171
l.u.b. 14
Landau, E. 146
Law, associative 5 75
Law, commutative 5 75 79
Law, distributive 5 75 78 88
Laws of order, fundamental 5 9
Least upper bound 14 26
Leibniz, G. W. 69
Leibniz’s test 68 138
lim inf 16
lim sup 16
Limes inferior 16
Limit form of the radical test 59
Limit of a convergent sequence 29
Limit point of a sequence 26
Limit point of a set 13
Limit theorem, Abel’s 109 145 169
Limit theorem, Cauchy’s 33 37 110 144
Limit, improper 30
Limit, lower 16 27
Limit, upper 16 27
Limiting value of a sequence 26
Logarithm, base of 54
Logarithm, Briggsian 167
Logarithm, calculation of 166
Logarithm, common 167
Logarithm, common, modulus of 167
Logarithm, natural 41 156
Logarithmic function 156
Logarithmic series 158
Lower bound 14
Lower bound, greatest 14 26
Lower limit 16 27
Lower order 30
L’Hospital’s Rule 35
Machin, J. 166
Machine, calculating 165 166
Maclaurin expansion 108
Maclaurin series 108
Main tests for sequences 37 38 43
Main tests for series 52 67
Majorant, convergent 77
Markoff, A.A. 87
Markoff’s transformation 88 172
Matrix, infinite 28
Matrix, row-finite 35
Matrix, triangular 35
MAX 15
Maximum 15
Mean 69
Merlens, F. 145
Method of comparison of coefficients 105
Method, bisection 39
Method, quadrisection 39
Metropolis, N.C. 165
MIN 15
Minimum 15
Modulus 10
Modulus of common logarithms 167
Molk, J. 175
Monotonic sequences, test for 38
Monotonically decreasing 19
Monotonically increasing 19
Multiple-valued function 158
Multiplication of convergent series 89 145
Natural logarithm 41 156
Natural logarithm, base of 54
Natural logarithm, calculation of 166
Natural number 1 4
Natural numbers, sequence of 18
Negative 5
Negative integer 4
Neighborhood 12
Neighborhood of point at infinity 26
Nested intervals, principle of 39
| Nested series 71
Nested squares, principle of 39
Nonabsolutely convergent product 98
Nondecreasing sequence 19
Nonenumerable set 27
Nonincreasing sequence 19
Norm-condition 35
Null sequence 19
Number axis 5
Number pairs 8
Number pairs, equality of 8
Number pairs, inequality of 8
Number pairs, product of 8
Number pairs, sum of 8
Number system 6
Number, complex 9
Number, complex, finite 26
Number, complex, polar form of 10
Number, complex, trigonometric representation of 10
Number, cut- 7
Number, irrational 7
Number, natural 1 4
Number, negative 5
Number, positive 5
Number, rational 4
Number, real 6 11
Numbers 6 10
Numbers, Bernoullian 118 119 174
Numbers, Eulerian 119
Numbers, field of real 7
Numbers, plane of complex 10
Numbers, prime 167
Numbers, sequence of 25
Numbers, sequence of natural 18
Numbers, set of 12 25
Numbers, set of real 13
Numbers, system of real 7
Numerical calculation 164
Numerical calculation of  165
Numerical calculation of e 165
Numerical calculation of natural logarithms 166
Numerical calculation of roots 167
Numerical calculation of trigonometric functions 168
Numerical evaluation of series 163 165
Odd function 105
Open interval 13
Open set 13
Operating with convergent series 74
Operating with power series 110
Operation, fundamental rules of 75
Operations, four fundamental 5
Order of summation, interchange of 87
Order, fundamental laws of 5 9
Order, lower 30
Order, same 30
Ordered field 5
Oscillating sequence 30
Oscillation between finite bounds 47
Oscillation between infinite bounds 47
Pairs, number 8
Parentheses, insertion of 45 75
Parentheses, removal of 75
Partial fraction 151
Partial integral 64
Partial product 48 92
Partial segment 67
Partial sum 45
Partial summation, Abel’s 70 130
Partial-fractions decomposition 155 156
Parts, integration by 130
Period 153
Period-strip 155
Permanent transformation 74 140
Plane of complex numbers 10
Plane, entire 99
Point at infinity 26
Point set, complex 19
Point set, real 19
Point, boundary 13
Point, interior 13
Point, isolated 13
Point, limit, of a sequence 26
Point, limit, of a set 13
Point, rational 5
Points, set of 12
Polar form of a complex number 10
Polynomial 90
Polynomial, quadratic 104
Positive 5
Positive number 5
Positive sequence 52
Power of a set 27
Power series 98 99
Power series, continuity of 102 107
Power series, differentiability of 107
Power series, functions represented by 102
Power series, identity theorem for 103
Power series, inversion of 119
Power series, operating with 110
Power series, reciprocal of 115
Power, general 150 158
Powers 11
Prime numbers 167
Principal value of amplitude 10
Principal value of arc sin z 160
Principal value of arc tan z 161
Principal value of general power 158
Principal value of natural logarithm 156
Principle of nested intervals 39
Principle of nested squares 39
Pringsheim, A. 125 175
Product of series, Cauchy 90 145
Product, absolutely convergent 96
Product, convergent 93
Product, divergent 97
Product, factor of 93 94
Product, infinite 4 48 92
Product, nonabsolutely convergent 98
Product, partial 48 92
Product, term of 94
Product, value of 93
Proper fraction 58
Proper subset 13
Proportional, asymptotically 30
Quadratic equation 8
Quadratic polynomial 104
Quadrisection method 39
Raabe’s test 136
Radial approach 109
Radian 168
Radical test 57
Radical test, limit form of 59
Radius of convergence 100
Ratio Test 57 58 129
Rational function 150 151
Rational number 4
Rational number system, extension of 7
Rational point 5
Real axis 10
Real domain 11
Real number 6 11
Real numbers , set of 13
Real numbers, field of 7
Real numbers, system of 7
Real numbers, system of, completeness theorem for 7
Real numbers, system of, theorem of continuity for 7
Real numbers, system of, uniqueness theorem for 7
Real part 10
Real point set 19
Real sequence 18
|
|
|
| Реклама |
|
|
|
|
|
О проекте