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

Maximum modulus      1
Maximum term      1
Mean domain      56 V 123
Mean value theorem      V 95 51 V V VI VI
Meissner, E.      250
Mertens, F.      351
Meusnier, M.Ch.      371
Mills, C.N.      372
Minkowski constant      IX 1.2 157 159
Minkowski, H.      56 157 159 371
Mittag-Leffler, G.      204
Modular graph      IV 172.1 28
Moebius function $\mu(n)$       VIII 34 118 VIII
Moebius, A.F.      118 313
Moment of a function      V 81 48
Montel, P.      237
Montmort, P.R.      306
Moore, E.H.      297
Muentz, Ch.H.      208
Muir, T.      280
Multiplication of Dirichlet series, Dirichlet      119
Multiplication of power series, Cauchy      119
Multiplicative arithmetical function      120
Multiplicative number theory      119
Nagy, J.v.Sz.      232
Neder, L.      361
Net rank      98 99
Netto, E.      313 314
Nevanlinna, F.      171
Nevanlinna, R.      171 195—197 198 211
Norm of a number in an algebraic number field      147
Normed mapping function      16 17
Number of distinct prime factors $\nu(n)$       118
Number of divisors $\tau(n)$       118
Number of zeros      1
Obreschkov, N.      211 251
Order of a trigonometric polynomial      72
Order of an entire function      IV 51 9 IV
Orthogonal linear transformation      106
Orthogonal matrix      106
Orthogonality condition for generalized Laguerre polynomials      VI 99 88
Orthogonality condition for Hermite polynomials      VI 100 88
Orthogonality condition for Jacobi (hypergeometric) polynomials      VI 98 87
Orthogonality condition for Legendre polynomials      86
Outer radius of a region      16 17
Paley, R.E.A.C.      211
Part      116
Partition of a number      AI 20.1 163
Peano curve      IV 170 28
Peano, G.      28
Periodic function      VI 32 76
Phragmen — Lindeloef method      32
Phragmen, E.      32
Picard exceptional value      IV 194 32
Picard, E.      32 35 211
Picard’s Theorem      IV 210 35 211
Pick, G.      195 197 342
Planck, M.      218
Plane of support      159
Plank’s law of radiation      V 43 218
Plemelj, G.      195
Poincare, H.      203 228 250 367
Point derive d’un point      IV 111 231
Polar, first      57
Polya, G., MD      314 317 373
Polya, G., MPR      239 249 257 298 318 337 352 353 372
Polynomial, integral-valued      129
Polynomial, irreducible      132
Polynomial, reducible      132
Polynomial, with integral coefficients      129
Power series with H-integral coefficients      140
Power series with integral coefficients      134 138
Power series with rational coefficients      134
Precise degree of polynomial      54
Prime divisor      130
Primitive power series with integral coefficients      VIII 155 137
Primitive roots of unity      VIII 36 118
Principal chord      IV 149 25
Prouhet, E.      303
Prufer, H.      247 342
Quadratic form      100
Quadratic non-residue      V 45 42
Quadratic residue      V 45 42
Quasilinearly dependent      100
Rabinowitsch, G.      349
Radicke      303
Radoe, T.      195 196 342
Rados, G.      283
Rational function      VIII 149 136 VIII
Rational independence      VIII 151 333
Recurrence relation      VI 87 86 VII
Recurrent determinant      96
Reducible polynomial      132
Region      IV 78 14
Relatively prime numbers      146
Relatively prime numbers, pairwise (coprime)      VIII 215 146
Remak, R.      287
Retali      281

Reversal of sign      39 V
Riemann hypothesis      VII 43.1 289 VIII
Riemann zeta function $\zeta(s)$       120 VIII
Riemann, B.      120 155 289 318
Riesz, F.      259
Riesz, M.      30 269 293 294 300
Riordan      290
Roberts, M.      280
Rodrigues, O.      86
Rodrigues’ formula      VI 84 86
Rolle, M.      36 37 43 47 51 60 213 229
Rolle’s Theorem      36 V 43 V 51 V V V
Rosenbaum, J.      366
Rotation theorem      IV 151 196
Roth, A.      205
Runge, C.      217
Sadier, J.      260
Sarantopoulos, S.      237
Saxer, W.      248
Scherrer, W.      354 355
Schlicht (univalent) function      IV 77 14
Schmidt, H.      211
Schoenberg, I.J.      218
Scholl, K.      369
Schreiber, M.      317
Schur, I.      203 238—240 247 251 266 267 286 289 292 294 326 327
Schwarz, H.A.      200 208 228
Serret, J.A.      324
Sidon, S.      359
Siegel, C.      251 324
simple harmonic motion      VI 61 80
Sine polynomial      72
Skolem, Th.      341 353
Slit region      IV 90 16 IV
Speiser, A.      336 354
Star-shaped closed curve      IV 133 22
Star-shaped region      IV 161 26 IV
Staudt, K.G.Ch.v.      339
Steinig, J.      218 226
Steinitz, E.      373
Stfickel, P.      325 330
Stieltjes integral      VII 66 297
Stieltjes, T.J.      228 297
Stirling numbers of the first and second kind      VII 54.2 107
Stirling, J.      9 107 180 181
Stirling’s formula      IV 50 9 IV IV
Stoll, A.      284
Study, E.      198
Suess, W.      367
Sum of divisors $\sigma(n)$       118
Sum of powers of divisors $\sigma_{a}(n)$       118
Support function      158 159
Supporting line      7
Sylvester, J.J.      223 224 303 305
Symmetric relation      VIII 221 147
Szaesz, O.      211 264 288 361
Szegoe, G.      195 211 237—239 250 252 258 283 298 300 342 360 361 367
Taylor, B.      361
Tchakalov, L.      210 211
Tchebotarev, N.      201 211
Tchebychev condition      VIII 154 137
Tchebychev polynomial      71 VI
Tchebychev theorem      VIII 249 153 VIII 358
Tchebychev, P.      71 81 137 153 264 358 361
Teixeira, F.G.      331
Titchmarsh (textbook)      10 211
Titchmarsh, E.C.      294
Toeplitz form      110 VII VII VII VII
Toeplitz, O.      110 298
Towber, J.      317
Transitive relation      VIII 221 147
Trigonometric polynomial      71—73 77 78
Turaen, P.      354
Unitary transformation      IV 207 34
UNITS      146
Univalent (schlicht) mapping      IV 77 14
Valiron, G.      167 171 208 247
Vandermonde determinant      V 48 43
Vandermonde, A.      43
Vertical pair      VII 22 97
Visible arc      IV 133 22
Walsh, J.L.      233
Weierstrass $\sigma(z)$ function      IV 49 9
Weierstrass preparation theorem      VIII 152 334
Weierstrass, K.      9 334
Weill, M.      331
Weyl, H.      352
Wiener, N.      211
Wilson, J.      339
Wilson’s Theorem      VIII 180 339
Wiman, A.      167 176 207 208
Wronski, H.      50 108 198 226 227 230
Wronskian determinant      V 87 50 108
Young, G.Ch.      361
Young, W.H.      256 361
Yule, U.      305
Zero of a polynomial      54 69
Zeta function $\zeta(s)$       120 VIII

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