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Polya G., Szego G. — Problems and Theorems in Analysis: Integral Calculus. Theory of Functions
Polya G., Szego G. — Problems and Theorems in Analysis: Integral Calculus. Theory of Functions

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Название: Problems and Theorems in Analysis: Integral Calculus. Theory of Functions

Авторы: Polya G., Szego G.

Аннотация:

Synopsis

From the reviews: "The work is one of the real classics of this century; it has had much influence on teaching, on research in several branches of hard analysis, particularly complex function theory, and it has been an essential indispensable source book for those seriously interested in mathematical problems. These volumes contain many extraordinary problems and sequences of problems, mostly from some time past, well worth attention today and tomorrow. Written in the early twenties by two young mathematicians of outstanding talent, taste, breadth, perception, perseverence, and pedagogical skill, this work broke new ground in the teaching of mathematics and how to do mathematical research. (Bulletin of the American Mathematical Society)


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 2004

Количество страниц: 392

Добавлена в каталог: 05.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel's theorem      I 86 21
Abel, N.H.      185 196 351 364
Ahrens, W.      174
Appell, P.      186
Archibald, R.G.      197
Argument principle      140
Audibert      217
Bagnera, J.      208
Bendixson, J.      361
Bernoulli numbers      I 154 35
Bernoulli's equation      III 90 121
Bernoulli, D.      121
Bernoulli, Jakob      35
Bernstein, S.      275 367
Bessel functions      I 97 II 16 97
Bessel, F.W.      22
BIaschke, W.      251 267
Bieberbach, L.      325
Biehler, Ch.      302
Binomial coefficients, Gaussian      11
Binomial coefficients, ordinary      6
Blumenthal, O.      376
Bohr, H.      372
Borel, E.      157 198 332
Brauer, A.      304
Brauer, R.      304
Briggs, H.      92 284
Buermann, H.      146
Burkhardt, H.      288
Burmann — Lagrange series      146
Cantor's discontinuum      III 130 206
Cantor, G.      206
Capacity      III 92 122
Caratheodory, C.      261 269 355 370
Carleman, T.      195 325 337 340 374
Carlson's theorem      III 328 170
Carlson, F.      380
Catalan, E.      176
Cauchy — Riemann differential equations      113
Cauchy, A.L.      64 68 111 113 119 133 146 221 245 248 312 317 326 330 337
Center of gravity of a mass distribution      108
Central subscript      27
Cesaro, E.      15 176 178 179 185 193 208 217 234 240
Change problem      19 174
Conformal center of gravity      III 129 130
Conformal mapping      115
Convergence exponent      25
Convex (concave) function      65
Cornu      142 342
Counting function      85
Cramer, H.      286
Csillag, P.      287 374
Darboux, G.      185 288
Dedekind, R.      309
Differences, finite      148 149
Dini's theorem      II 126 81
Dini, U.      81 269
Direction of accumulation      III 52 112
Dirichlet series      I 75 III III 18 78 153
Dirichlet — Mehler formula      III 167 135
Dirichlet, P.G.L.      18 78 111 112 135 153 240 246 309 333
Enestroem, G.      301
Enlargement, area      117
Enlargement, linear      116
Enveloping series      32
Equidistribution      87
Euler's (or Mascheroni's) constant      II 19.1 II 51 54
Euler's function $\varphi(n)$      II 188 93
Euler, L.      50 51 54 57 174 177 178 186 234 240 243 348 349
Faber, G.      376
Farey series      II 189 93
Farey, J.      93
Fatou, P.      369
Fejer, L.      200 253 260 272 281 303 337
Fekete, M.      198 302 359
Fine, N.J.      228
Force, flux of      III 89 120
Force, lines of      III 86 120
Fourier constants      II 141 83
Fourier, J.      83 253
Franel, J.      234 275 283 284
Frank, Ph.      326
Fredholm, I.      247
Frobenius, G.      196
Fujiwara, M.      304
Gamma-function $\Gamma(s)$      II 31 II 54 84
Gauss, C.F.      11 186 187 303
Goursat, E.      313
Graeffe's method II      95.4 257
Greenstreet,E.      183
Gutzmer. A.      324
Haar, A.      206
Hadamard's three circle theorem      III 304 164
Hadamard, J.      164 166 309 376
Hamburger's function      III 153 III 332 360
Hamburger, H.      332 360
Hansen, P.A.      97
Hardy, G.H.      179 195 208 247 251 257 332 359 376
Harnack, A.      363
Heeke, E.      280
Hermite, Ch.      104 180 182 288 302 332
Hermitian form      III 7 104
Hewitt, E.      206
Hilbert, D.      265 337
Hille (textbook)      140 195 269 338 339 376 379
Hobson, E.W.      77 259
Hoelder, O.      68 249
Hurwitz — Courant (text;book)      146 195 238 312 336 338 376
Hurwitz, A.      274 301 341 346
Inequality, Cauchy's      II 80 68
Inequality, Cauchy's, Hoelder's      II 81.1 68
Inequality, Cauchy's, Minkowski's      II 90 71
Inequality, Cauchy's, Schwarz's      II 81 68
Integral, definite      46
Integral, improper      52
Integral, multiple      60
Jacobi polynomials      III 219 147
Jacobi, C.G.J.      147 186 187 214 349
Jacobsthal, E.      217
Jensen's formula      III 175 138
Jensen, J.L.W.V.      130 138 248 268 305 324 326 339 340
Jordan, C.      239 246
Julia, G.      344 373
Kakeya,S.      206 301
Kempner, A.      205
Kirchhoff, G.      320
Knopp (textbook)      198 206 208 234 306 309 362
Knopp, K.      205
Koebe, P.      369
Koenig, D.      286
Koenig, J.      358
Kojima, T.      111
Kurschak, J.      254
Lacour, E.      186
Lagrange (Buermann) series      145
Lagrange, J.L.      145 146 347
Laguerre polynomials      III 219
Laguerre, E.      147 180 257 302
Laisant, C.A.      218
Landau, E.      212 271 276 356 357
Laplace equation      III 87 120
Laplace, P.S.      96 120 136 288 294 317 334
Lasker, E.      209
Lattice points      I 28 5 13
Laurent, P.A.      151
Lebesgue, H.      288
Legendre polynomials      III 157 III 135 147
Legendre polynomials, zeros      II 191 94
Legendre, A.M.      94 95 97 135 147 328
Lerch, M.      273 274
Levy, P.      311
Lindeloef, E.      218 368 369 379
Line of support      I 110 202 126
Linear transformation of sequences      15
Linear transformation of sequences, convergence preserving      111
Linear transformation of sequences, luwer (upper) triangular      I 79 194
Linear transformation of sequences, matrix      I 66 I 15 19
Linear transformation of sequences, regular      I 68 I 16 19
Linear transformation of sequences, triangular      I 66 15
Littlewood, J.E.      195 247 251 257
Lowner, K.      300 326 373
Lucas, Ch.F.      303
Lukacs, F.      253
Lukacs, Th.      323
Lvel lines      III 85 120
Macdonald, H.M.      343 344
Maclaurin, C.      33 34 212 243
Mahrcnholz, J.      242 330
Majorant (minorant) series      14
Mapping      113
Markoff, A.A.      286
Maximum principle III      136 131
Maximum term      27
Means, arithmetic, geometric, harmonic of functions      II 48 57 63
Means, arithmetic, geometric, harmonic of numbers      57 62 63
Mehler, F.G.      135 333
Mercator's projection      116
Mercator, G.      116 313
Mertens, F.      308
minimax      101
Minkowski, H.      71 261
Mises, R. V.      280 294
Modular graph      130
Moivre, A.      292
Moments of a function      II 138 83
Moreau, C.      216
Nagy, J.v.Sz.      305
Netto, E.      180
Nevanlinna, F.      339 340 381
Nevanlinna, R.      339 381
Noerlund, N.E.      192 361 366
Obreschkoff, N.      347
Orthogonal functions      III 117 127
Oscillation      II 106 77
Ostrowski, A.      342
Ouspenski, J.      211
Paoli, P.      180
Parscval, M.A.      324
Partition of a set      42
Pascal, B.      147
Perron, O.      197 288
Persson, P.      379
Phragmen — Lindeloef method      III 322 166
Phragmen, E.      273 379
Pincherle, S.      221
Pit      III 132 131
Plancherel, M.      274
Poisson's formula      III 173 138
Poisson, S.D.      138
Polya, G., HSI:      173
Polya, G., MD:      178 189 223
Polya, G., MPR:      227 344
Polynomial with integral values      I 128 29
Postage Stamp Problem      I 9 174
Potential      III 86 120
Pringsheim, A.      329
Prufer, H.      281 360 364
Radcmacher, H.      208
Rassicod, L.      180
Rearrangement of infinite series      30 112
Regular sequence      86
Riemann's $\zeta$-function      II 46 56
Riemann, B.      46 56 77 113 119 172 208 259 260 311 312 326 343
Riesz, F.      337
Riesz, M.      367
Rotation      117
Rouche's theorem      III 194 142
Rouche, E.      142 344
Rumpcn, H.      218
Saddle point      III 132 131
Saxer, W.      201
Schiffer, M.      256
Schlegel, V.      182
Schlicht (univalent, simple) function      117
SchoH, K.      360
Schottky, F.      366
Schur, I.      111 193 215 216 218 268 302 308 309 337 353
Schwarz's lemma      III 280 160
Schwarz, H.A.      68 369
Schweitzer, P.      263
Scott, G.A.      33
Sidon, S.      309
Sierpinski, W.      208
Slowly increasing (decreasing) function      II 150 85
Sommerfeld, A.      121 142 320 342
Star-shaped      III 109 125
Steinhaus, H.      111
Steinitz, E.      258 280 311
Step-function      II 102 76
Stereographic projection      III 60 115
Stieltjes, T.J.      288 305 308 332
Stirling's formula (for $\Gamma$)      II 205 97
Stirling's formula (for $\Gamma$), numbers, 1st kind      43
Stirling's formula (for $\Gamma$), numbers, 2nd kind      42
Stirling's formula (for $\Gamma$), series      I 165 36
Stirling, J.      36 42 43 234 289 351 366
Stream function      III 86 120
Stream function, lines      III 85 120
Stream function, potential      III 86 120
Sturm, Ch.      341
Subseries      28
Subseries, complementary      31
Sum, upper, lower      46 60
Support function      126
Support function, line of      I 110 202 126
Szasz, O.      218
Szegoe, G.      200 214 242 266 268 264 287 333 376
Szuecs, A.      286
Takagi, T.      304
Taylor, B.      267 281
Threlfall, W.      208
Toeplitz. O.      16 111 303 366
Univalent (schlicht, simple) function      117
Valiron. G.      201
Variation, total, of a function      II 9 232
Vector field      113 119
Vector field, conjugate potential      III 85 120
Vector field, irrotational      119
Vector field, potential      III 86 120
Vector field, solenoidal      120
Veress, P.      200
Vitali, G.      218
Volterra, V.      231
Wallis' formula      II 202 289
Wallis, J.      289
Walther. A.      379
Waring. E.      179
Watson, G.N.      33 233 330 343
Weierstrass' approximation theorem      II 136 II 83
Weierstrass, K.      83 200
Weighing problem      I 9 174
Weyl, H.      211 279 280 281 286 333 337
Whittaker — Watson (textbook)      36 64 146 212 246 343 366
Wiener, F.      337
Wiman, A.      201
Winding number      140
Winternitz, A.      316
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