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| Knopp K. — Theory and applications of infinite series |
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| Предметный указатель |
Integration by parts 169
Integration, term by term 176 341
interval 20
Interval of convergence 153 327
Interval of definition 158
Intervals, nest of 21 394
Inverse-sine function 215 421
Inverse-tangent function 214 422
Isomorphous 10
Jacobi, C.G.J. 439
Jacobsthal, E. 244 263
Jensen, J.L.W.V. 74 76 441
Jones, W. 253
Jordan, C. 16
Karamata, J. 501 504
Keplerian motion 546
Kneser, A. 550
Knopp, K. 2 75 241 244 247 267 350 404 448 467 477 481 487 507 547
Kogbetliantz, E. 488
Kowalewski, G. 2
Kronecker, L., complement to theorem of 150
Kronecker, L., theorem of 129 485
Kummer's transformation of series 247 260
Kummer, E.E. 241 247 260 311
Lacroix, S.F. 550
Lagrange, J.L. 298
Laguerre, E. 550
Lambert, J.H. 448 451
Lambert, J.H., series 448 seq.
Landau, E. 2 4 11 444 446 452 484
Laplace, P.S. 546
Lasker, E. 490
Law of formation 15 37
Law of induction 6
Law of monotony 6
Laws of arithmetic 5 32
Laws of order 5 29
Le Roy, E. 473
Lebesgue, H. 168 350 353
Leclert 247
Left differentiability 163
Left hand continuity 161
Left limit 159
Legendre, A.M. 375 520
Leibniz, G.W. 1 103 131 193 244 457
Leibniz, G.W., equation of 214
Leibniz, G.W., rule of 131 316
Length 169
Levy, P. 398
LIMIT 64 462
Limit of a function 159 403—404
Limit of a sequence 64
Limit of a series 101
Limit theorems see "Abel" "Cauchy" "Toeplitz"
Limit, on the left, right 159
Limit, upper, lower 92—93
Limitable 462
Limitation processes 463—477
Limitation processes, general form of 474
Limiting curve 330
Limiting point of a sequence 89 394
Limiting point, greatest, least 92—93
Lipschitz, R. 368 371
Littlewood, J.E. 407 478 501
Loewy, A. 2 4
Logarithmic differentiation 382
Logarithmic scales 278 seqq.
Logarithmic series 211 seq. 419
Logarithmic tests 281—284
Logarithms 57—59 211 420
Logarithms, calculation of 24 198 254—257
Lyra, G. 487
Machin, J. 253
Maclaurin, C. 521
Main criterion of convergence, first for sequences 80
Main criterion of convergence, first for series 110
Main criterion of convergence, second for sequences 84 87 393 395
Main criterion of convergence, second for series 126—127
Main criterion of convergence, third for sequences 97
Malmsten, C.J. 316
Mangoldt, H.V. 2 350
Mantissa 68
Markoff's transformation of series 242—244 265
Markoff, A. 241 242 265
Mascheroni's constant see "Euler's constant"
Mean value theorem of the differential calculus, first 164
Mean value theorem of the integral calculus, first 168
Mean Value Theorem, second 169
Measurable 169
Mercator, N. 104
Mertens, F. 321 398
Method of bisection 39
Mittag-Leffler, G. 1
Mobius' coefficients 446 451
Modulus 8 390
Molk, J. 556
Moments, Stieltjes' problem of 549
Monotone 17 44 162—163
Monotone, fully 263—264 305
Monotony, law of 5 6
Monotony, p-fold 263—264
Motions of x 160
Multiplication 6 31 50
Multiplication of infinite series 146 seq. 320
Multiplication of power series 179
Multiplication, term by term 70 135
Napier, J. 58
Natural numbers see "Numbers"
Nest of intervals 21 394
Nest of squares 394
Neumann, C. 17
Newton, I. 1 104 193 211 457 556
Noerland, N.E. 521
Non-absolutely convergent 136 396—397 435
Null sequences 17 45 60—63 72 74
Number axis 8
Number concept 9
Number corpus 7
Number system 9
Number system, extension of 11 34
Numbers see also "Bernouilli's numbers" "Euler's
Numbers, complex 388 seq.
Numbers, irrational 23 seq.
Numbers, natural 4
Numbers, prime 14 445 451 548
Numbers, rational 3 seqq.
Numbers, real 33 seqq.
Numerical evaluations 79 232—273 especially
Odd functions 173
Ohm, M. 184 320
Oldenburg 211
Olivier, L. 124
open 20
ordered 5 29
Ordered aggregate 5
Oscillating series 101—103
Oscillation 159
Pair of tests 308
Partial fractions, expansion of elementary functions in 205—208 239 377 419
Partial products 105 224
Partial summation, Abel's 313 397
Partial sums 99 224
Partitions, number of 548
Passage to the limit term by term 338 seqq. see "Subtraction" "Multiplication" "Division" "Differentiation" "Integration"
Peano, G. 11
Period strip 413 seq. 416—418
Periodic functions 200 413
Permanence condition 463
Perron, O. 105 475 478 546
Poincare, H. 520 536 543 550
| Poisson, S.D. 521
Poncelet, J.V. 244
Portion of a series 127
Postulate of completeness 34
Postulate of Eudoxus 11 27 34
Power series 151 seqq. 171 401
Powers 49—50 53 423
Prime numbers 14 445 451 548
Primitive period 201
Principal criterion see "Main criterion"
Principal value 420—426
Pringsheim, A. 2 4 86 96 175 221 291 298 300 301 309 320 399 490 556
Problem of moments 559 seq.
Problems A and B 78 105 230
Products 31
Products with arbitrary terms 221 seq.
Products with complex terms 434 seq.
Products with positive terms 218 seq.
Products with variable terms 380 seq. 436
Products, infinite 104 218—229
Pythagoras 12
Quotient 31
Quotient of power series 182
Raabe, J.L. 285
Rademacher, H. 318 548
Radian 59
Radius of convergence 151
Radix fractions 37 seq.
Radix fractions, breaking off 249
Radix fractions, recurring 39
Raff, H. 475
Ramunujan, S. 548
Range of action 463
Range of summation 398
Rapidity of convergence see "Convergence"
Ratio Test 116—117 277
Rational functions 189 seq. 410
Rational numbers see "Numbers"
Rational-valued nests 28
Real numbers see "Numbers"
Rearrangement 47 138
Rearrangement in extended sense 142
Rearrangement of products 227
Rearrangement of sequences 47 70
Rearrangement of series 136 seqq. 318 398
Rearrangement, Riemann's 318 seq.
Rearrangement, theorem, main 143 181
Rearrangement, theorem, main, application of 236—240
Reciprocal 31
Regular functions 408
Reiff, R. 104 133 457
Remainders, evaluation of 250 259 526 531—535
Representation of real numbers on a straight line 33
Representative point 33
Reversible functions 163 184
Reversion theorem for power series 184 405
Riemann's  -function 345 444—446 491—492 531 538
Riemann's rearrangement theorem 318—320
Riemann's theorem on Fourier series 363
Riemann, B. 166 318 319 363
Riesz, M. 444 477
Right hand continuity 161
Right hand differentiability 163
Right hand limit 159
Rogosinski, W. 350
Root test 116—117
Roots 50 seqq.
Roots, calculation of 257—258
Runge, C. 556
Saalschutz, L. 184
Sachse, A. 353
Scales, logarithmic 278 seqq.
Scherk, W. 239
Schlomilch, O. 121 287 320
Schmidt, Herm. 212
Schnee, W. 481
Schroter, H. 204
Schur, L. 267 481 547
Section 40 99
Seidel, Ph.L.v. 334
Semi-convergent 520 536
Sequences 14 43
Sequences of functions 327 seqq. 429
Sequences of points 15
Sequences of portions 127
Sequences, bounded 16
Sequences, complex 388 seqq.
Sequences, convergent 64—78
Sequences, divergent 65
Sequences, infinite 15
Sequences, null 17 seqq. 45 60—63 72 74
Sequences, rational 14
Sequences, real 15 43
Series for trigonometrical functions 198 seq. 414
Series of analytic functions 428
Series of arbitrary terms 126 seqq. 312
Series of complex terms 388 seqq.
Series of positive terms 110 seqq. 274
Series of positive, monotone decreasing terms 120 seqq. 294
Series of variable terms 152 seq. 326 428
Series, alternating 131 250 263 316 518
Series, asymptotic 535 seqq.
Series, binomial 127 190 208 423
Series, Dirichlet 317 441
Series, divergent 457 seqq.
Series, exponential 148 191 411
Series, faculty 446 seq.
Series, Fourier 350 seqq. 492
Series, geometric 111 179 189 472 508
Series, harmonic 81 112 115—117 150 237 238
Series, hypergeometric 289
Series, infinite 98 seqq.
Series, infinite sequence of 142
Series, Lambert 448 seq.
Series, logarithmic 211 seq. 419
Series, transformation of 240 seqq. 260
Series, trigonometrical 350 seq.
Sierpinski, W. 320
Similar systems of numbers 10
Sine 199 seq. 384 414
Sine product 384
Squares, arrangement by 90
Steinitz, E. 398
Stieltjes' moment problem 549
Stieltjes' series 549
Stieltjes, Th.J. 238 302 321 530 545 549 554
Stirling's formula 529 seq. 538 541
Stirling, J. 240 448 530
Stokes, G.G. 334
Stolz, O. 4 39 76 87 311 407 556
Strips of conditional convergence 444
Sub-sequences 46 92
Sub-series 116 141
Subsidiary value 421
Subtraction 5 31
Subtraction, term by term 48 71 135
SUM 30
Sum of a series 101 seq. 462
Sum of divisors 451
Summability, boundary of 492
Summable 462
Summable, absolutely 513
Summable, uniformly 496
Summation by arithmetic means 460 seqq.
Summation formula, Euler's 518 seqq.
Summation of Dirichlet series 464 491
Summation of Fourier series 464 492
Summation problem for asymptotic series 543 548
Summation processes 464—476
Summation processes, commutability of 509
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