Polya G. — Problems and Theorems in Analysis: Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry :: Электронная библиотека попечительского совета мехмата МГУ

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Polya G. — Problems and Theorems in Analysis: Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry

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Название: Problems and Theorems in Analysis: Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry

Автор: Polya G.

Аннотация:

From the reviews: "... In the past, more of the leading mathematicians proposed and solved problems than today, and there were problem departments in many journals. Pólya and Szego must have combed all of the large problem literature from about 1850 to 1925 for their material, and their collection of the best in analysis is a heritage of lasting value. The work is unashamedly dated. With few exceptions, all of its material comes from before 1925. We can judge its vintage by a brief look at the author indices (combined)

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 392

Добавлена в каталог: 09.04.2008

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Предметный указатель

Additive number theory      119
Ahlfors, L.V.      182 202 206 211
Ahrens, W.      356
Algebraic conjugate      145
Algebraic degree of      145
Algebraic differential equation      100
Algebraic field      145
Algebraic function      100 135
Algebraic integer      143
Algebraic number      143
Apolar      59
Arithmetic mean      IV 66 11 V
Arithmetical function      111 118
Associated polynomials      67
Asymptotic value of an entire function      31
Baelint, E.      249
Baschwitz 317
Basis polynomials of interpolation      82 VI
Beke, E.      285
Bellman, R.      318
Bemays, P.      360
Beraha, Sami.      292
Bernoulli numbers      VIII 182 141 VIII
Bernoulli, Jak.      141 155
Bernstein, S.      30 84 209 269
Bernstein’s Theorem      IV 179 30 84
Bessel functions      IV 73 13 V V
Bessel, F.W.      62 64
Bieberbach, L.      192—197
Bieri, H.      366
Binomial coefficients      134
Blaschke, W.      367 371 377 378
Blichfeldt, H.F.      355
Boas, R.P.      167 175
Bohr, H.      203
Borel, E.      284
Brauer, A.      325 327—329
Brauer, R.      325 327—329
Brisse, Ch.      325
Brun, Viggo      314
Bunyakovski, V.      304
Caratheodory, C.      17 300
Carleman, T.      206 207 208 208
Carlson, F.      337
Catalan, E.      331
Cauchy product      119 VIII 40 42
Cauchy, A.L.      29 119 193 196 207 244 279 311 352
Cayley, A.      104
Center of gravity of mass distribution      V 101 53 V
Center of gravity of mass distribution of polynomial      54 V
Center of gravity of mass distribution with respect to a point      53 V V V V V
Center of similitude      V 122 56
Central index (subscript)      1 V
Central point      17
Cesaero (textbook)      376
Cesaero, E.      312 318
Change of sign      36 39
Characteristic equation      VII 48 105
Characteristic function      113
Characteristic root of matrix      IV 210 35
Chrestenson, H.E.      356
Christoffel formula      VI 88 270 VI VI VI
Christoffel, E.B.      270 273—275
Circular convexity      V 104 54 V
Circular domain      53 V V V V
Circular-arc polygon      V 103 53 V
Clausen, Th.      339
Closed system of functions      IV 212 35
College d'Aberystwyth      281
Concave functions      VI 36 76
Conformal center of gravity      23
Congruence between power series      140
Congruence of numbers      147
Conjugate algebraic numbers      145
Conjugate numbers in a field      147
Conn, A.      330
Constant sign, function of      39
Convex domain      V 126 57 158
Convex function      VI 36 76
Convex mapping      IV 162 198
Coprime (pairwise relatively prime) numbers      146 VIII
Cosine polynomial      72
Coxeter, H.S.M.      56
Cross sum of a number      VIII 172 139
Crossing point of a function      39
Curtiss, D.R.      249
Curvature bound      IV 163 27
Cut      IV 90 16 17
Cyclotomic polynomial      VIII 36 118 VIII VIII VIII VIII
Dallot, A.      313
de Moivre, A.      306
de Rochas      325
Degree of an algebraic number      145
Degree of parity      VIII 251 358—359
Denjoy, A.      206
Derivative of polynomial with respect to a point      57
Derived system      58
Descartes, R.      36 39 41 42 46 50 51 66 226 227
Descartes’ Rule of Signs      V 36 41 46 50 V V 66 V
DeUac, H.      367
Diagonal pair      VII 22 97
Diophantes      154 163 164
Diophantine equation      VIII 255 154 AI AI AI
Dirichlet product      119 VIII VIII VIII VIII VIII
Dirichlet series      V 78 47 118—120 V VIII VIII
Dirichlet, P.G.L.      47 118—120 129 131 148 149 224 250 311 313 315 316 319 323
Divisor      116 146
Divisor, greatest common      116 146
Domain      20 IV
Egervaery, J.      237 239
Eisenstein, G.      134—137 149 150 304 326 332 333
Eisenstein’s condition      135 VIII VIII VIII VIII VIII VIII VIII VIII
Eisenstein’s Criterion      VIII 120 326
Eisenstein’s theorem      135 VIII VIII VIII
Elliptic function $\varphi(z)$       VIII 184 142
Enlargement ratio      17 IV
Entire function      IV 180 30 IV IV IV IV IV IV IV
Entire function, asymptotic value of      31
Enveloping expression      VIII 27.1 115
Enveloping series      V 163 63
Epstein, P.      293
Errera, A.      315 333
Euler, L.      118 130 154 155 306 307 312 318 322 360 380
Euler’s (or Mascheroni’s) constant —Г'(1)      VIII 260 155
Euler’s function $\varphi(n)$       VIII 25 115 118
Even function      VI 36 76
Exceptional value of an entire function      IV 210 35
Exponent of convergence      IV 58 10 IV
Faber, G.      192—195
Fatou, P.      335 337 351
Fejer, L.      225 232 237 255 256 259 261—264 269 272
Fekete, M.      218 233 249 259 269 283
Feller, W.      308
Fibonacci numbers      VII 53 106 VIII
Fibonacci, L.      106 138
Field      143 145
Fine, N.J.      367
Finite rank      98
Fleck, A.A.      359
Flugel, W.      326
Fourier coefficients      75 VI
Fourier series      75 VI VI VI VI 32 33 257 IX
Fourier system of functions      IV 212 35
Fourier, J.      35 76 109 257 258 368
Franel, J.      260 341
Frobenius, G.      315 323 330
Fueter, R.      355
Fujiwara, M.      288 340
Function, integral-valued      130
Gaedecke, W.      373

Gallai, T.      354
Gauss, C.F.      14 56 109 123 151 160 232 304 315 325 360 369 371 382
Gaussian curvature      IX 10 160 IX 371
Gaussian error curve      IV 76 14
Gauss’s Formula      IX 8 369
Gauss’s theorem      V 121 56 V
Generating number of an algebraic number field      145
Genus of an entire function      10 IV
Geometric mean      IV 64 11 IV V
Gmelin, O.      330
Goldbach, Chr.      322
Goluzin, G.M.      182
Goursat, E.      260
Grace, J.H.      57 237 238
Grace’s theorem      57
Gram, J.P.      297
Grandjot, K.      351
Greatest common divisor      116 146
Greatest common part      116
Grenander, U.      298
Grommer, J.      219 289
Gronwall, T.H.      195 196 198 255 256
Grosch, W.      325
Gross rank      98
Gummer, C.F.      297
H-integral (Hurwitz-integral) coefficients of a power series      140
Hadamard, J.      10 30 171 207 283 338
Hadamard’s gap theorem      VIII 173 338
Hadamard’s three-circle theorem      IV 177 30
Halphen, G.H.      267
Hankel determinant      96
Hankel, H.      96 98
Hansen, D.      338
Harary, F.      279
Hardy, G.H.      2S0
Hardy-Wright (textbook)      42 143 145 315 317 319 358
Harmonic series      VIII 250 153 VIII
Hausdorff, F.      194 260
Heawood, P.J.      238
Hecke (textbook)      145—147 150 325 330 346 349 352 353
Heine, E.      333 334
Hensel, K.      331
Hermite polynomials      V 58 44 V VI VI
Hermite, Ch.      44 56 103 110 260 276 299 303
Hermitian determinant      VII 70 211
Hermitian form      VII 43 103 110 V
Hidden arc      IV 133 22
Hilbert, D.      330 349
Hille, E.      (textbook) 9 10 211
Hirsch, A.      373—376 378
Hoelder, O.      280
Homothetic circular discs      V 122 56
Horizontal pair      VII 22 97
Horseshoe-shaped curve      IV 145 24
Hurwitz condition      VII 154 137
Hurwitz, A.      137 140 205 212 237 239 244 280 287 289 309 330 335 340 356 356 357 359 362
Hurwitz-Courant (textbook)      9 142 202 204 217 239 240 347
Hypergeometric (Jacobi) polynomials      VI 98 87
Hypergeometric series      VIII 146 136
Inclusion and exclusion principle      113
Index of change      36 V1 39
Inner measure      IV 81 182
Inner radius of a region      16 17
Integer, algebraic      143
Integral coefficients, polynomial with      129
Integral domain      143
Integral part of a number      111
Integral-valued function      130
Integral-valued polynomial      129
Interpolation formula, Lagrange      82
Irreducible polynomial      VIII 112 131 132 145
Irreducible polynomial in two variables      VIII 234 150
Iversen, F.      205 206
Jackson, D.      255 256
Jacobi (hypergeometric) polynomial      VI 98 87 VI
Jacobi (Legendre) symbol $(\frac{n}{p})$       V 45 42 VIII VIII VIII 99 102 VIII
Jacobi, C.G.J.      42 87 252 274 313 360
Jensen, J.L.W.V.      170 240
Jensen’s Inequality      IV 32 170
Jentzsch, R.      233 325 335 338
Jordan content      VIII 242 151
Jordan, C.      250
Jump points of the central index      5
Kaerteszi, F.      354
Kakeya, S.      341
Kempner, A.J.      354
Kluyver, J.C.      339
Kneser, H.      201
Knight, B.W.      317
Koch, H.V.      204
Koebe distortion theorem      23 IV
Koebe image region      16
Koebe, P.      16 23 183 184 194 195
Koenig, J.      303
Kollros, L.      359
Kowalewski (textbook)      262 283—286 290 296 299
Kowalewski, G.      374
Kritikos, N.      289
Kronecker, L.      284 346
Kuerschaek, J.      358 371
Lagrange interpolation formula      82 VI VI VIII VIII VIII
Lagrange, J.L.      82 84 266 321 325 365
Laguerre generalized      VI 99 88 VI
Laguerre polynomials      V 58 44
Laguerre, E.      44 46 54 57 88 212 215 216 219 222 224—226 230—232 239 249 275 318
Lambert series      VIII 65 125
Lambert, J.H.      125
Landau, E.      29 30 201 203 224 237 324 331 335
Laplace, P.S.      86
Laplace’s formula      VI 86 86
Lattice point      112 VIII 128
Lattice point in space      152
Lattice point in the plane      150
Laurent series      343
Laurent, P.A.      199 343
Least common multiple      116
Lebesgue constants of a Fourier series      VI 35 76
Lebesgue, H.      76 303 344
Left-adjacent integer [x]      VIII 6 111
Legendre (Jacobi) symbol      V 45 42 VIII VIII VIII
Legendre polynomials      V 58 44 V 85 VI VI VI VI VI VI 97 VI
Legendre, A.M.      42 44 56 85—87 134 154 239 270 330 360
Lehmer, D.H.      351
Leibniz formula      VI 85 269 VII
Leibniz, G.W.      269 296 317
Lemniscate function      VIII 184 142
Levi, E.E.      379
Levinson, N.      211
Lindeloef, E.      32 183 207
Linear dependence      100 144
Liouville function $\lambda(n)$       119
Liouville, J.      119
Lipschitz condition      IX 25 162
Lipschitz, R.      162
Littlewood, J.E.      197 208 250
Loewner, K.      190 193 194 198 370 371
Lucas, E.      331 353 359
Lukaecs, F.      260 278
Macdonald, H.M.      247
Maclaurin series      V 163 63
Maclaurin, C.      63 223
Malmquist, J.      204
Malo, E.      239
Mangoldt function $\Lambda(n)$       119
Mangoldt, H.V.      119
Mantel      312
Marden, M.      230
Markov theorem      84
Markov, A.A.      84 269
Mascheroni, L.      155

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