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| Szego G. — Orthogonal polynomials |
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| Предметный указатель |
Laurent expansion 252
Lawton 151 409
Lebesgue 14 15 409.
Lebesgue constant 13 258 330 336 338 339 350
legendre v 70 409. Polynomials
Leibniz, rule of 67 68 101
Lengyel 113. See Erdos — Lengyel
LeRoy 103 409
Level curve 8
Limited operation 12
Linear operation see Operation
Liouville — Stekloff, method of 202 ff. 210 299
Lipschitz 383
Lipschitz condition 6 162 163 186
Lipschitz — Dini condition 279 297 324
Littlewood see Hardy — Littlewood — Polya
Locher 363 420
Lorch xi 190 249 420
Lorch — Muldoon — P. Szego 158 420
Lorch — P. Szego 158 420
Lukacs 4 178 249 409
Magnus — Oberhettinger 420
Makai 20 148 157 190 420 421
Makai — Turan 158 421
Marcinkiewicz 273 330 347 409
Markoff, A. v 33 37 50 57 115 116 121 122 139 259 378 409
McGregor see Karlin — McGregor
Mean approximation 10 11
Mean-value theorem 383
Mean-Value theorem of Gauss 275 310 311
Mean-Value theorem, second 2 202 357 363
Mechanical quadrature v ix 12 14 58 187 329 348
Mechanical quadrature for classical abscissas 352 ff
Mechanical quadrature for Jacobi abscissas 355 ff. 378 379
Mechanical quadrature, Gauss — Jacobi 47 ff. 111 348
Mehler iii 47 49 85 192 380 394 409 410
Mehler — Heine see Asymptotic formula
Meixner 34 35 410
Method of Liouville — Stekloff see Liouville — Stekloff
Method of steepest descent 202 203 221
Modulus of continuity 6 7 335 336 340 346
Moecklin 194 203 410
Moment problem of Stieltjes, iii, iv, v 40
Muckenhoupt 190 243 273 421
Muckenhoupt — Stein 273 421
Muldoon see Lorch — Muldoon — P. Szego
Muntz 251 410
Myller — Lebedeff 251 410
Neumann, E.R. 130 251 380 410
Neumann, F. 248
Neumann, J. von 108
Newman — Rudin 273 421
Newton's formula 259
Norm function see Weight function
Norm of operation 12
Normalization 28 58 160
Novikoff 394 396 421
Obrechkoff 198 248 249 410
Olver 243 421
Operation, linear functional 11 ff
Orthogonal polynomials and continued fractions 54 ff
Orthogonal polynomials, asymptotic formula of v ix 4 296
Orthogonal polynomials, Christoffel — Darboux formula for 42 ff
Orthogonal polynomials, classical 29 49
Orthogonal polynomials, closure 40 108
Orthogonal polynomials, definition ix 23
Orthogonal polynomials, expansion in series of v ix 28 38 39 41 311 312 313
Orthogonal polynomials, extremum properties of 28 38
Orthogonal polynomials, general properties of 38 ff
Orthogonal polynomials, highest coefficient of 28
Orthogonal polynomials, recurrence formula for 42 ff. 55 391
Orthogonal polynomials, representation of 27
Orthogonal polynomials, zeros of v ix 44 121 188 189
Orthogonality, Orthogonalization v vi 8 23 44
Orthonormal set 23 25 68
Osgood — Caratheodory's theorem 364
P-function, contiguous Riemann 71
Parabola of convergence 253
Parseval's formula 40 289 368
Peano 1
Peetre 110 421
Pencil 49
Perron 45 54 144 202 410
Perron's formula for Laguerre polynomials 198 199 202 203 220 221 225
Planch erel 250
Plancherel — Rotach 132 201 203 410
Pochhammer — Barnes, notation of 103
Poincare 310
Poisson's integral 276 292.
Pollaczek ix 37 393 421
Pollard 273 421.
Polya — Szego vii 5 11 21 24 34 40 70 87 105 117 134 135 175 178 179 184 212 310 311 411
Polya, vii 42 53 117 134 154 166 350 388 410 411.
Polynomials associated with a curve (Tchebichef polynomials) 368 385
Polynomials orthogonal on a curve vii 364 Zeros
Polynomials orthogonal on a segment see Orthogonal polynomials
Polynomials orthogonal on the unit circle ix 287 384
Polynomials, classical v 29 159. Expansion Mechanical
Polynomials, Faber 372 374
Polynomials, Fejer's generalization of Legendre see Fejer
Polynomials, Gegenbauer see Polynomials ultraspherical
Polynomials, Hermite vi ix 29 36 37 105 110 111 176 190 331 388 392. Differential Expansion Generating Interpolation Recurrence Rodriques' Zeros
Polynomials, Jacobi vi ix 3 29 58 94 103 105 107 161 167 172 179 243 249 295 348 383 385 399. Differential Expansion Generating Interpolation Mechanical Recurrence Rodrigues' Zeros
Polynomials, Krawtchouk 35 ff
Polynomials, Laguerre vi ix 29 35 100 110 111 164 176 184 185 190 243 379 380 382 387 391 393 395. Differential Expansion Generating Interpolation Recurrence Rodrigues'
Polynomials, Legendre vi 29 30 33 34 48 58 63 70 85 95 96 136 162 164 167 172 189 346 348 379 382 392 393. Expansion Generating Integral Interpolation Zeros
Polynomials, of S. Bernstein and Szego 31 ff
Polynomials, Poisson — Charlier 34 35 37 377 389 390
Polynomials, Pollaczek 37 393
Polynomials, Stieltjes — Wigert 33
Polynomials, Tchebichef (of the first and second kind) 3 26 29 30 60 63 112 136 162 347 348 387 391. Interpolation Zeros
Polynomials, ultraspherical, vi 29 58 80 93 107 135 167 170 379 387 390 394. Differential Expansion Generating Integral Interpolation Recurrence Rodrigues' Zeros
Popoviciu 46 140 142 411
Principle of argument 21 157
Probability, calculus of 35
Quadratic form 24 123 187 366
Quadratic form of Hankel (recurrent) type 27 309
quantum mechanics iii
Rabinowitz see Davis — Rabinowitz
Rau 197 214 249 411
Recurrence formula of Hermite polynomials 106
Recurrence formula of Jacobi functions of second kind 78 ff. 379
Recurrence formula of Jacobi polynomials 71 ff
Recurrence formula of Laguerre polynomials 101
Recurrence formula of polynomials orthogonal on the unit circle 293
Recurrence formula of ultraspherical polynomials 81 82
Recurrence formula, general 42 ff
Riemann see Integral P-function
| Riemann's lemma 254 267 319
Riemann's theory of trigonometric series 248
Riesz, F. 12 275 411
Riesz, M. 5 57 304 411
Robin's constant see Transfinite diameter
Rodrigues' formula for Hermite polynomials 106
Rodrigues' formula for Jacobi polynomials 67 ff. 73 74 94 99 117
Rodrigues' formula for Laguerre polynomials 101 117 388
Rodrigues' formula for ultraspherical polynomials 81
Roever vii
Rogosinski 347
Rolle's theorem 51 53 117 378
Roosenrad 110 421
Ross vii
Rotach 203 249 250 411.
Rouche's theorem 21 149
Rudin see Newman — Rudin
Runge 7
Runge — Walsh, theorem of 7
Saddle-point 219 231
Sapiro 98 421
Sarmonov 392 421
Scalar product 8 9 10 25 365 367 378
Schmeiser 158 422
Schmidt, E. 34 35 411
Schoenberg 273
Schoenberg — Szego 190 422
Schur, I. vi 140 142 411
Schwid 204 416
See Lorch — P. Szego, Lorch — Muldoon — P. Szego
Seidel — Szasz 94 422
Sen — Rangachariar 145 411
Series, Jacobi vi 273
Series, Laguerre 240
Series, Legendre vi 42. Orthogonal
Sherman 57 411
Shibata 145 412
Shohat v vii 42 48 159 163 189 309 333 336 340 345 347 350 385 386 412
Shohat — Hille — Walsh 422
Singular integral 13
Smirnoff 275 276 289 368 369 412
smith 412
Sonin 96 100 102 104 159 166 169 176 189 379 412
Spencer 132 412
Statistics, mathematical v
Stein see Muckenhoupt — Stein
Steinig see Askey — Steinig
Stekloff 9 210 350 412.
Stekloff — Fejer, theorem of 350 ff. 360
Step function 34 35 37 164
Step polynomial 329 339
Step polynomial, generalized 331
Stieltjes v 33 37 46 50 51 53 54 58 87 89 90 92 93 121 136 139 140 142 145 151 156 165 172 174 175 193 195 211 382 412 413. Hermite Integral Laplace Moments Polynomials
Stirling's formula 227
Stirling's series 212
Stone 10 23 251 413
Strip of convergence 253
Studden see Karlin — Studden
Sturm — Liouville type 210
Sturm's theorem (method) on zeros vi 45 111 121 124 139
Sturm's theorem on differential equations 19 ff
Summability see Abel Cesaro
Suranyi — Turan 347 422
Szasz 5 190 413 422.
Szego — Turan 157 158 422
Szego, G. 19 27 31 33 37 45 59 87 93 94 96 110 125 127 128 135 137 140 158 163 164 167 189 190 197 198 203 206 214 243 248 249 251 274 287 289 294 299 300 309 310 312 313 340 346 355 360 361 366 369 371 377 384 388 392 393 394 413 414 422. Grenander Karlin Polya Polynomials Schoenberg
Szego, P. xi
Tamarkin vii ix 42 414
Tchakaloff 189 383 414
Tchebichef v 33 47 50 54 70 100 186 188 189 414. Polynomials
Thome 243 422
Titchmarsh 37 57 301 310 311 415
Toeplitz matrix 287 399
Toeplitz operator 99
Total variation 12 34 35
Transfinite diameter 364 369
Tricomi ix 242 243 415 422
Trigonometric polynomials 3 5 11
Trigonometric representation 90 ff.
Turan, vii, ix 158 190 388 389 422. Egervary Erdos Grunwald Makai Suranyi Szego
Uniqueness theorems 248
Uspensky 53 107 203 219 220 251 415
Van Veen 132 204 415
Vector 9
Vector space 10
Vietoris 363 422
Vitali — Sansone 415 423
Vitali's theorem 57
Volterra equation 211
Wainger see Askey — Wainger
Walsh 7 366 415.
Wangerin 84 415
Watson 18 20 96 102 104 107 159 162 192 193 202 203 222 251 253 363 380 384 415.
Webster 347 423
Weierstrass, theorem of 5 ff. 10 110
Weight function 9 37 68 159 160 162 185 188 287 294 296 297 299 309 312 314 316 347 380 385
Weiss, G. see Coifman — G. Weiss
Weyl 110 251 310 415
Whittaker — Watson 14 ff. 58 63 65 66 71 75 84 86 88 93 103 248 415
Widom — Wilf 243 423
Wigert 33 102 251 413.
Wilf see Widom — Wilf
Williamson see Csordas — Williamson
Wiman 131 416
Winston 131 351 416
Wintner see Hartman — Wintner
Wright 203 384 416
Young, W.H. 10 248 414
Zernike 132 416
Zero-function 9 40 45
Zeros of Airy's function 18 19 377 382
Zeros of analytic functions 21
Zeros of Bessel functions 126 ff. 140 192 193 381
Zeros of Hermite polynomials 117 ff. 123 127 141 240 353
Zeros of Jacobi polynomials, vi 116 ff. 140 144 192 193 237 250 379 381
Zeros of kernel polynomials 369 377
Zeros of Laguerre polynomials 116 ff. 122 127 141 150 237 353 381 382
Zeros of Legendre functions of second kind 155 ff
Zeros of Legendre polynomials 111 122 125 353
Zeros of numerators of continued fractions 57
Zeros of polynomials orthogonal on a curve 369
Zeros of polynomials orthogonal on the unit circle 292 384
Zeros of solutions of differential equations see Sturm's theorem
Zeros of Tchebichef polynomials 330 351
Zeros of ultraspherical polynomials 119 121 138 352 381.
Zeros, distribution of, v 310
Zeros, electrostatical interpretation of 140 382
Zygmund 248 253 254 274 276 279 281 359 416 423
“Gegenbeispiel” 250 272
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