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| Szego G. — Orthogonal polynomials |
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| Предметный указатель |
Abel 100 401
Abel's continuity theorem 92
Abel's transformation 2 91 135
Abelsummability 245 273.
Achieser 5 37 42 401 416
Adamoff 203 248 249 250 401
Addition theorems 58 97
Additive operation 11 12
Airy's function 18 19 131 201 234 239 243 377 382.
Antipole condition 246 249 265
Approximation 5 ff
Askey xi 98 99 110 273 348 363 391 392 416
Askey — Fitch 96 363 416
Askey — Gasper 97 99 110 190 392 417
Askey — Pollard 273 417
Askey — Steinig 97 158 363 417
Askey — Wainger 99 190 273 417
Associated function, Legendre 84
Asymptotic formula of Bessel functions 15 16
Asymptotic formula of classical polynomials 191 ff
Asymptotic formula of general orthogonal polynomials v vi 296
Asymptotic formula of Hermite polynomials 132 191 194 198 218 235 242
Asymptotic formula of Jacobi functions of second kind 201 225
Asymptotic formula of Jacobi of Hilb's type 169 197 202 214
Asymptotic formula of Jacobi of Mehler — Heine type 167 192 202.
Asymptotic formula of Jacobi polynomials 58 167 168 191 201 202 212 225
Asymptotic formula of kernel polynomials 369 ff
Asymptotic formula of Laguerre polynomials 132 191 193 194 198 236 237 240
Asymptotic formula of Laguerre polynomials of Hilb's type 177 199 203 216 219 384
Asymptotic formula of Laguerre polynomials of Mehler — Heine type 193 194 217
Asymptotic formula of Laguerre polynomialsof Plancherel — Rotach type 200 201 227 Perron's
Asymptotic formula of Legendre functions of second kind 198 212 222
Asymptotic formula of Legendre polynomials 191 193 194 243
Asymptotic formula of Legendre polynomials of Hilb's type 195 202 212 Laplace
Asymptotic formula of polynomials orthogonal on a curve 371 ff
Asymptotic formula of polynomials orthogonal on the unit circle 297 ff
Asymptotic formula of ultraspherical polynomials 196. 197 206 208 209 212
Bailey 273 392 417
Balazs — Turan 347 417
Banach 13 401
Bateman 96 98 99 273 417
Bateman Project ix 95 110 243 393 394 417
Bernstein's theorem on trigonometric polynomials 5 280 304.
Bernstein, S. vi 9 31 42 159 165 168 296 299 300 303 314 315 330 401
Bessel functions v 14 95 96 102 126 140 166 167 191 193 202 203 212 225 243 272 353 362 363 380 384 387 392 400. Zeros
Bessel's inequality 25 38 289 316 322 333 367
Blumenthal 268 310 401
Bochner 108 273 401 417
Bonami — Clerc 273 417
Bottema 132 401
Bounded variation, functions of 12
Brauer, A. 131 401
Bruns 122 125 136 138 401
Buell 124 ff. 401
Butlewski 166 417
Capacity see Transfinite diameter
Caratheodory 364 402.
Carleman 366 402
Carleson 273 417
Cauchy — Hadamard formula 248 253 312
Cauchy's principle value 278
Cauchy's theorem 69 106 221 275 289 324 370 372
Centroid 189
Cesaro summability vi 244 246 258
Cesaro summability (means) of Fourier series 12 14 246 250
Cesaro summability (means) of Hermite series 250 251
Cesaro summability (means) of Jacobi series vi 246 248 249 256
Cesaro summability of Laguerre series 247 248 250 251 271
Cesaro summability of Legendre series 14 249
Cesaro summability of power series 325
Cesaro summability of ultraspherical series 248
Characteristic values 49 187
Charlier see Polynomials
Christoffe, formula of 29 ff. 397
Christoffel iii 42 43 47 402
Christoffel ( — Darboux) formula 42 ff. 318 326
Christoffel numbers 46 ff. 114 115 187 351 378
Clerc see Bonomi — Clerc
Closure see Orthogonal polynomials
Coifman — G. Weiss 273 417
Completely monotonic sequence 136 ff. 155
Confluent hypergeometric function 104
Conformal mapping 21 160 364 365 372
Conjugate function 279
Conjugate points (interpolation) 332 347
Continued fractions v 54
Continuous operation 12
Convergence in mean 330
Convergence in mean, generalized 330
Convergence of interpolation 330
Convergence, quadrature 330 333 350
Convergent (continued fraction) 55 ff
Cotes numbers 12 349 363
Courant — Hilbert see Hilbert — Courant
Cramer 251 402
Csordas — Williamson 388 418
Darboux 42 43 195 196 211 402
Darboux method 202 206 265 269 395
Darboux's formula for Jacobi polynomials 168 196 225 236 237 248 253 337 353
Davis — Hirschman 99 418
Davis — Rabinowitz 158 418
de la Vallee-Poisson summability 273
DeBruijn 110 418
Deviation, quadratic 38 41 288
Deviation, Tchebichef 41 368
Differences 34 35 136
Differential equation v 16 37 152 159 164 166 210
Differential equation of Bessel functions 15
Differential equation of Hermite polynomials 106 176 380
Differential equation of Jacobi'(hypergeometric) polynomials iv 60 117 141
Differential equation of Laguerre polynomials 100 117 176
Differential equation of ultraspherical polynomials 80 81
Dirichlet 85 402
Dirichlet — Mehler see Integral representation
Dirichlet's integral 12 14
Discriminant of classical polynomials 143 ff
distribution 8 9 26 29 38 40 57 181 274 330 351 378
Distribution of Stieltjes type 9 33 38
Doetsch 34 35 380 402 418
Du Bois, Reymond 14 402
Eagleson 37 418
Egervary — Turan 348 418
ellipse 8 21 251
Ellipse of convergence 245 248 252 311 312
Elliptic functions, v 60
Equiconvergence 31 244 246 247 249 313
Erdelyi ix 104 243 273 380 402 418
Erdelyi — Swanson 243 418
Erdos vii 347 348 418
Erdos — Feldheim 334 402
Erdos — Grunwald 347 418
Erdos — Lengyel 347 418
Erdos — Turan 113 114 115 332 333 335 347 348 402 418
Euler 72 402
Euler's constant 15
Euler's integral of second kind see Gamma function
Euler's integral of the first kind 14
expansion v vi 58
Expansion in power series 313 314
Expansion in series of classical polynomials 244 ff. 251
Expansion in series of general orthogonal Hermite polynomials 244 245 247 251 253 269
Expansion in series of general orthogonal polynomials 313 ff
Expansion in series of Jacobi polynomials 244 ff
Expansion in series of Laguerre polynomials 244 ff. 249 253 266 313
Expansion in series of Legendre polynomials 248 249
Expansion in series of Tchebichef polynomials 248 314
Expansion in series of ultraspherical polynomials 248 249. Orthogonal
Expansion, finite cosine, of Legendre polynomials 90 ff
Expansion, infinite sine, of Legendre polynomials 90 ff
Faber 299 330 368 369 372 402.
| Fatou 275 403
Fatou's theorem 274
Favard 43 403
Fejer vii 14 45 58 89 91 96 134 136 157 165 172 174 175 179 198 202 249 264 330 336 348 350 386 403.
Fejer — Szego 175 404
Fejer's asymptotic formula for Laguerre polynomials 198 202 203 237 240 269
Fejer's generalization of Legendre polynomials 135 ff. 174 206
Fejer's integral 12
Fejer's representation of positive trigonometric polynomials 3 4 274
Fejer's representation of positive trigonometric polynomials, generalization of 275 ff
Fejer's second generalization of Legendre polynomials 137 138 155
Fekete 369 404
Feldheim 95 96 97 334 335 386 404 418.
Fitch see Askey — Fitch
FOURIER v
Fourier coefficient (constant) 24 287
Fourier series 12 14 24 25 28 38 39 244 246 253 274 289 311 314 323 347 367.
Fourier's inversion formula 387
Freud 309 418
Friedrichs 404
Fujiwara 145 404
Functions of second kind, Jacobi's 73 ff. 251
Functions of second kind, Legendre's 74 78 88 89 92 379 383. Integral Zeros
Fundamental polynomials of Hermite interpolation 330 ff
Fundamental polynomials of Lagrange interpolation 12 47 329
Galbrun 251 404
Gamma-function 14 75
Gasper 37 98 99 190 273 419.
Gatteschi 242 419
Gauss iii 33 47 49 62 404. Mechanical
Gauss — Weierstrass summability 273
Gegenbauer 80 94 98 99 404
Generating function 35 36
Generating function of Hermite polynomials 106 380
Generating function of Jacobi polynomials 69 ff. 82 83 95
Generating function of Laguerre polynomials 101 202 379
Generating function of Legendre polynomials 90 206 207 383
Generating function of Pollaczek polynomials 393
Generating function of ultraspherical polynomials 82 83
Geometric mean 275 296 385
Geronimus 42 189 404
Gibbs' phenomenon 251
Ginibre 392 419
Gottlieb 37 405
Grenander — Szego 274 287 419
Griinbaum 392 419
Griinwald vii 330 347 405 419.
Griinwald — Turan 346 405
Gronwall 165 249 405
Haar 14 248 405
Hahn, W. 33 107 111 112 129 132 151 405 419
Hamburger 57 110 405
hankel see Quadratic form
Hardy 102 380 405
Hardy — Littlewood — Polya 2 405
Hartman — Wintner 20 419
Hausdorff 136 155 405
Heine iii 27 37 47 54 80 90 151 192 194 251 405
Heine — Stieltjes theorem, iv 151 ff
Helly 13 405
Helly's theorem 13 14 258 272 330 339 350
hermite v 156 405 406
Hermite interpolation 330 ff. 340 347 348
Hermite — Stieltjes 89 156 157 172 406
Hermitian form 287
hilb 195 249 406
hilbert 142 145 406
Hilbert — Courant 58 59 100 106 109 406
Hildebrandt 8 10 406
Hille 102 105 126 131 242 251 406.
Hirschman 99 273 419.
Hobson iv 58 84 92 382 406
Hollo 335 406
Horton 99 273 419
Howell 392
Hsu 390 419
Hua 99 419
Hunt 273 420
Hurwitz, theorem of 21 150 193 239 371
Hypergeometric function, iii 62 ff. 83 84 96.
Inequalities 159 ff
Inequality for the arithmetic and geometric mean 2 300
Inequality, Abel's 2 174 205
Inequality, Cauchy's 2 39 120 160 183 291 302 306 321 370
Inequality, Schwarz's 2 9 110 136 162 268 276 317 376
Inequality, Turan's 190 388.
Integral equations v 218 251
Integral representation of Legendre functions of second kind 88 ff
Integral representation of Legendre polynomials 85 ff
Integral representation of Legendre polynomials, Dirichlet — Mehler 85 ff. 96
Integral representation of Legendre polynomials, Laplace (first) 86 176
Integral representation of Legendre polynomials, Laplace (second) 86 ff
Integral representation of Legendre polynomials, Stieltjes 87 fl"
Integral representation of ultraspherical polynomials, Dirichlet — Mehler 89
Integral representation of ultraspherical polynomials, Stieltjes 89 ff
Integral, Lebesgue vii 9 26 159 246 274 275 287 291 364 384
Integral, Riemann 9 10 280 281 282 298 310 333 335 351 361
Integral, Riemann — Stieltjes 8 9 11 50 333 350 351
Integral, Stieltjes — Lebesgue v 1 8 10 38 187
Interpolation v ix 12 14 58 329 347
Interpolation on Hermite abscissas 340
Interpolation on Jacobi abscissas 335 ff
Interpolation on Laguerre abscissas 340 344
Interpolation on Legendre abscissas 386
Interpolation on Tchebichef abscissas 330 334 335 386
Interpolation on ultraspherical abscissas 386. See Conjugate points Fundamental Hermite Lagrange
Interpolation, Lagrange 12 47 180 329 348 349 389
Jackson vii 6 7 42 331 406
Jacob 251 406
Jacobi, iii 49 58 69 86 406 407. Mechanical Polynomials Series
Jensen's theorem 301
Joo 391
Jordan arc 8 364
Jordan curve 8 21 364 365
Jordan — Pochhammer integral 75
Jordan, C. 58 407
Jordan, Ch. 34 407
Julia 369 407
Kaczmarz — Steinhaus 1 10 407
Kanter vii
Karlin — McGregor 37 273 389 420
Karlin — Studden 5 420
Karlin — Szego 190 388 420
Keldysch — Lawrentieff 368 407
Kernel polynomials 39 40 44 71 101 180 183 249 290 322 323 333 351 368 377. Zeros
Klein 145 407
Kogbetliantz 102 168 172 203 240 248 249 251 256 273 380 407
Koornwinder 98 99 420
Korous 131 132 162 167 212 251 303 408
Koschmieder 60 408
Kowalewski 24 408
Kowallik 251 408
Krall 107 408
Krawtchouk 113 408.
kronecker 408
l'Hospital, rule of 307
Lagrange 100 408
Lagrange polynomials 329 ff. 347
Lagrange series 70. See Interpolation
Laguerre 100 117 131 408 409.
Lame function 151
Langer 204 210 409
Laplace iv 86
Laplace series 96 249
Laplace series, transform 379. See Integral representation
Laplace — Heine formula 194 204 208 243
Laplace — Heine formula, generalization 194
Laplace's formula for Legendre polynomials 194 198 201 202 204 211 224
Laplace's formula for Legendre polynomials, Darboux's generalization 195 201 206 211
Laplace's formula for Legendre polynomials, Stieltjes' generalization 195 202 209
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