Watson G.N. — Treatise on the theory of Bessel functions :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Watson G.N. — Treatise on the theory of Bessel functions

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Treatise on the theory of Bessel functions

Автор: Watson G.N.

Язык:

Рубрика: Математика/Анализ/Специальные функции/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1922

Количество страниц: 812

Добавлена в каталог: 06.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Products of Bessel functions, expansions of arbitrary functions into series of      525 572
Products of Bessel functions, integrals representing      31 150 221 438 439 440 441 445 446 448
Products of Bessel functions, series of      30 151 152
Products of Weierstrassian factors, Bessel functions expressed as      497
Puiseux, V.      559
Quotient of Bessel functions, expressed as a continued fraction      153 154 303
Radius vector of an orbit, expansion as trigonometrical series of the mean anomaly      6 13 552 553 554
Raffy, L.      94
Ramanujan's integrals of Bessel functions with respect to their order      449
Ramanujan's method of evaluating definite integrals      382
Ramanujan, S.      382 449
Random flights, problem of      419
Rank of Bessel functions and cylinder functions      129
Rawson, R.      91
Rayleigh, Lord      50 55 56 74 95 137 155 157 189 230 231 233 331 333 374 389 395 419 421 477 502 510 511 616 618 660
Real variables, expansions of arbitrary functions of      see “Dini series” “Fourier “Neumann “Schloemilch
Reality of zeros of Bessel functions      482 483 511
Reciprocation formulae for Lommel's functions of two variables      542
Recurrence formulae      see also “Functional equations” “Hemi-cylindrical “Three-term
Recurrence formulae for Anger's functions      311
Recurrence formulae for Bessel coefficients      17
Recurrence formulae for Bessel functions of the first kind      45
Recurrence formulae for Bessel functions of the second kind      66 71
Recurrence formulae for Bessel functions of the third kind      74
Recurrence formulae for Bessel functions with imaginary argument      79
Recurrence formulae for Bourget's functions      326
Recurrence formulae for Cauchy's numbers      325
Recurrence formulae for cylinder functions      82
Recurrence formulae for Gegenbauer's polynomials      283
Recurrence formulae for Lommel's functions      348
Recurrence formulae for Lommel's functions of two variables      539
Recurrence formulae for Lommel's polynomials      298 303
Recurrence formulae for Neumann's polynomials       274
Recurrence formulae for Neumann's polynomials ${\Omega}_n (t)$       283
Recurrence formulae for Schlaefli's functions      71 342 343
Recurrence formulae for Schlaefli's polynomials      285
Recurrence formulae for Struve's functions      329
Recurrence formulae for Weber's functions      311
Recurrence formulae for Whittaker's functions      339
Reduced functions, Cailler's      536
Remainders in asymptotic expansions, magnitudes of      206 211 236 314 332 352
Remainders in asymptotic expansions, signs of      206 207 209 215 315 333
Remainders in asymptotic expansions, Stieltjes' approximations to      213
Repetition of zeros of Bessel functions and cylinder functions, impossibility of      479
Riccati's differential equation      1 2 85—94
Riccati's differential equation, connexion with Bessel's equation      1 90
Riccati's differential equation, equation cognate to      91
Riccati's differential equation, generalised      3 92 94
Riccati's differential equation, generalised, cross-ratio of solutions      94
Riccati's differential equation, generalised, equivalence with the linear equation of the second order      92
Riccati's differential equation, generalised, singularities of      94
Riccati's differential equation, generalised, soluble by various numbers (two, one or none) of quadratures      3 93
Riccati's differential equation, limiting form of      86
Riccati's differential equation, soluble cases of (D. Bernoulli's)      85
Riccati's differential equation, soluble cases of, exhausted by D. Bernoulli's formula and its limit      123
Riccati's differential equation, solutions by various mathematicians (Buler)      87
Riccati's differential equation, solutions by various mathematicians (Cayley)      88
Riccati's differential equation, solutions by various mathematicians (D. Bernoulli)      2 85 89
Riccati's differential equation, solutions by various mathematicians (Schlaefli)      90
Riccati's differential equation, solved by means of infinite series by James Bernoulli      1
Riccati's differential equation, transformations of      86
Riccati, J.F.      1 2 3 85 86 87 88 94
Riemann — Lebesgue lemma, analogues of the      457 471 589 599
Riemann's theorem on trigonometrical series, analogues for Schloemilch series      642 647
Riemann's theorem, analogues for series of Fourier — Bessel and Dini      649
Riemann, G.F.B.      80 158 172 203 229 235 427 457 486 623 637 649
Riesz, M.      606 614
Rodrigues' transformation      see “Jacobi's transformation”
Rodrigues, O.      27
Roehrs, J.H.      10
Rudski, P.      477 508
Russell, A.      81 82 204
Rutgers, J.G.      373 374 375 376 380 579
Rybczynski, W. von      56 225 449
Sasaki, S.      507
Savidge, H.G.      82 204 658
Schafheitlin's discontinuous infinite integral      398 402 405 406 408 411
Schafheitlin's integrals, representing Bessel functions and cylinder functions      168 169 490 491 493
Schafheitlin, P.      64 137 142 168 169 207 215 373 391 392 398 401 402 406 408 421 447 477 479 482 485 487 489 490 491 492 493 494 508 510 543
Scheibner, W.      6
Schlaefli's functions and       71 340 343
Schlaefli's functions of negative order      343
Schlaefli's functions, addition theorems for      344 345
Schlaefli's functions, differential equations, satisfied by      342 343
Schlaefli's functions, recurrence formulae for      71 342 343
Schlaefli's hypergeometric function      90
Schlaefli's polynomial       284 286
Schlaefli's polynomial, addition theorem for      289
Schlaefli's polynomial, connexion with Neumann's polynomial       285 286
Schlaefli's polynomial, Crelier's integral representation of      288
Schlaefli's polynomial, differential equation, satisfied by      285
Schlaefli's polynomial, expression by means of Bessel functions      287
Schlaefli's polynomial, expression in terms of Lommel's function      350
Schlaefli's polynomial, integrals evaluated in terms of      350
Schlaefli's polynomial, recurrence formulae for      285
Schlaefli's solution of Riccati's equation      90
Schlaefli, L.      10 14 27 28 30 32 33 63 64 65 67 72 79 90 91 143 145 151 160 171 174 175 176 178 179 181 185 195 196 215 216 228 253 274 276 278 284 285 286 288 289 290 341 342 344 345 508 577 579 581 582 583 585
Schloemilch series      618—649
Schloemilch series, definition of      621
Schloemilch series, definition of generalised      623
Schloemilch series, expansion of an arbitrary function of a real variable into      619 623 629
Schloemilch series, nature of convergence of      637 645
Schloemilch series, null-functions, expressed by      634
Schloemilch series, Riemann's theorem on trigonometrical series (analogue of)      642 647
Schloemilch series, special cases of      632
Schloemilch series, symbolic operators in the theory of      626 627
Schloemilch series, theory of functions of complex variables connected with      623
Schloemilch series, uniqueness of      643 647
Schloemilch, O.X.      14 18 33 34 35 36 153 173 183 617 618 619 621 622 628 655 656
Schoenholzer, J.J.      145
Schott, G.A.      551 556 572 573
Schwarz, K.H.A.      358 643
Schwarzschild, K.      361
Schwerd, F.M.      477 654
Searle, J.H.C.      199
Segar, H.W.      483
Series containing Bessel functions      see “Dini series” “Fourier “Kapteyn “Neumann “Schloemilch
Series of Bessel functions, definition of      580
Series of positive terms, approximation to the sum of (greatest term method)      8
Serret, J.A.      171 173 188
Sharpe's differential equation      105
Sharpe's differential equation, solution by generalised hypergeometric functions      105
Sharpe, H.J.      105 157
Sheppard, W.F.      199 454 579 595 615
Siacci, F.      92
Siemon, P.      328 398
Sign of remainders in asymptotic expansions      206 207 209 215 315 333 449
Sign of Struve's function      337 417
Sine-integral, expressed as a series of squares of Bessel coefficients      152
Singularities of functions defined by Neumann series (Pincherle's theorem)      526
Singularities of the generalised Riccati equation      94
Smallest zeros of Bessel functions      5 500 516
Smith, Bernard A.      655
Smith, Clara E.      621
Smith, Otto Andreas      50
Sommerfeld's expansion      see “Kneser — Sommerfeld expansion”
Sommerfeld, A.J.W.      56 57 178 361 389 395 406 417 464 499
Sonine — Mehler integrals, representing Bessel functions      169 170
Sonine's definite integral      373
Sonine's definite integral, generalised      382
Sonine's discontinuous infinite integrals      415
Sonine's infinite integrals      432
Sonine, N.J.      82 83 132 137 139 143 169 170 171 175 176 177 180 279 280 281 290 353 354 362 363 367 373 374 375 376 377 378 383 386 391 394 395 398 401 411 415 417 418 431 432 433 434 439 454
Sound, Sharpe's differential equation in the theory of      105
Spherical geometry, used to express Bessel functions as limits of Legendre functions      155
Spherical geometry, used to obtain transformations of integrals      51 374 376 378
Spitzer, S.      68 71 153
Squares of Bessel functions      see “Products of Bessel functions”
Stability of a vertical pole associated with Bessel functions of order one-third      96
Stationary phase, applied to Bessel functions      231 233

Stationary phase, method of      225 229
Stearn, H.      482 621
Steepest descents, applied to Bessel functions      237 241 244 245 262
Steepest descents, applied to functions of Anger and Weber      316
Steepest descents, applied to Struve's function      333
Steepest descents, connexion with Laplace's method of approximation      421
Steepest descents, method of      235
Steiner, L.      655 661
Steinthal, A.E.      171 387
Stephenson, A.      579
Stern, M.A.      500
Stieltjes, T.J.      195 196 207 208 209 213 214 464
STIRLING, JAMES      7 8 214
Stokes' method of computing zeros of Bessel functions and cylinder functions      503 505 507
Stokes' phenomenon of the discontinuity of arbitrary constants      201 203 238 336
Stokes, George Gabriel      8 12 53 55 68 69 70 80 95 97 188 189 195 201 202 225 229 238 320 324 336 391 405 503 505 507 605 659
Strutt, J.W.      see “Eayleigh”
Struve's function $H_{\nu} (z)$       328
Struve's function $H_{\nu} (z)$ of order ±(n + 1/2)      333
Struve's function $H_{\nu} (z)$ with imaginary argument      329 332
Struve's function $H_{\nu} (z)$ with large argument and order, asymptotic expansions of      333
Struve's function $H_{\nu} (z)$ with large argument, asymptotic expansions of      332
Struve's function $H_{\nu} (z)$ , connexion with Weber's function      336
Struve's function $H_{\nu} (z)$ , differential equation, satisfied by      329
Struve's function $H_{\nu} (z)$ , inequalities connected with      328
Struve's function $H_{\nu} (z)$ , infinite integrals containing      392 397 417 425 436
Struve's function $H_{\nu} (z)$ , integral representations of      328 330
Struve's function $H_{\nu} (z)$ , occurrence in generalised Schloemilch series      622 623 631 645 646 647
Struve's function $H_{\nu} (z)$ , recurrence formulae for      329
Struve's function $H_{\nu} (z)$ , sign of      337 417
Struve's function $H_{\nu} (z)$ , tables of      663 666—697
Struve's function $H_{\nu} (z)$ , Theisinger's integral for      338
Struve's function $H_{\nu} (z)$ , zeros of      479
Struve's infinite integrals      396 397 421
Struve, H.      328 329 333 337 392 396 397 417 661
Sturm's methods of Lommel's polynomials      304 305 306
Sturm's methods, applied to determine the reality of zeros of Bessel functions      483
Sturm's methods, applied to estimate the value of the smallest zero of Bessel functions and cylinder functions      517 518
Sturm, J.C.F.      304 477 479 517 518 521
Suchar, P.J.      90
Svanberg, A.F.      173
Symbolic operators in expressions representing Bessel functions      50 170
Symbolic operators in expressions representing solutions of various differential equations      41 51 108
Symbolic operators in the theory of Schloemilch series      627
Tables (references to) of Airy's integral      659
Tables of       663 698—713
Tables of Bessel coefficients and functions, derivable from them      654 655 656 658
Tables of Bessel coefficients of order n      664 730—732
Tables of Bessel coefficients of orders 0 and 1      662 666—697
Tables of Bessel coefficients with equal order and argument      664 746
Tables of Bessel functions of orders n + 1/2, -n - 1/2      658 659
Tables of Bessel functions of orders ±1/3, ±2/3      659
Tables of Bessel functions of orders ±1/4, ±3/4      659
Tables of Bessel functions of the first kind of order 1/3      664 714—729
Tables of Bessel functions of the first kind of orders n + 1/2, -n - 1/2      664 740—741
Tables of Bessel functions of the second kind      655 656 658
Tables of Bessel functions of the second kind of order 1/3      664 714—729
Tables of Bessel functions of the second kind of order n      664 732—735
Tables of Bessel functions of the second kind of orders 0 and 1      662 666—697
Tables of Bessel functions of the second kind with equal order and argument      664 747
Tables of Bessel functions of the third kind      657
Tables of Bessel functions of the third kind of order 1/3      664 714—729
Tables of Bessel functions of the third kind of orders 0 and 1      662 666—697
Tables of Bessel functions with imaginary argument      657 658
Tables of Bessel functions with imaginary argument of order 1/3      664 714—729
Tables of Bessel functions with imaginary argument of order n      664 736 737—739
Tables of Bessel functions with imaginary argument of orders 0 and 1      663 698—713
Tables of Fresnel's integrals      661 664 744—745
Tables of integrals of Bessel functions and Struve's functions      661
Tables of integrals of Bessel functions of order zero      664 752
Tables of Lommel's functions of two variables      660
Tables of Struve's functions of orders 0 and 1      663 666—697
Tables of Thomson's functions ber x and bei x, etc.      658
Tables of zeros of Bessel coefficients and functions of integral order n and of order 1      664 748—751
Tables of zeros of Bessel coefficients, functions and associated functions      659 660
Takeuchi, T.      313
Tannery, J.      11 156 302
Theisinger's integral representation of Bessel functions      184
Theisinger's integral representation of Struve's and Weber's functions      338
Theisinger, L.      184 185 338
Thomson's (Sir William) functions with large argument, asymptotic expansions of      203
Thomson's (Sir William) functions, ber z, bei z      81
Thomson's (Sir William) functions, connexion with Bessel functions      81
Thomson's (Sir William) functions, generalisations      81
Thomson's (Sir William) functions, references to tables of      658
Thomson's (Sir William) functions, squares and products of      82 148
Thomson, Joseph John      65 173
Thomson, William      see “Kelvin”
Three-term relations connecting Bessel functions, cylinder functions and Lommel's polynomials      300 301
Tisserand, F.      371
Todhunter, L.      27 157 199
Transcendants, elementary, definition of      111
Transcendants, order of      111
Transcendants, solutions of differential equations by      112
Transitional regions, associated with Bessel functions of large order      248
Turriere, E.      15
Unferdinger, F.      310
Uniformity of convergence of Dini series      601
Uniformity of convergence of Fourier — Bessel series      593 594
Uniformity of convergence of Kapteyn series      575
Uniformity of convergence of Schloemilch series      632
Uniqueness of Fourier — Bessel and Dini series      616 649 651
Uniqueness of Schloemilch series      643 647
Upper bounds      see “Inequalities”
Valewink, G.C.A.      196
Van Vleck, E.B.      480
Vandermonde, A.      102
Verdet, E.      477
Vessiot, E.      94
Viscous fluid, motion of, associated with Airy's integral      189
Volterra, V.      579 621
Voronoi, G.      200
Voss, A.      406
Wagner, C.      13 142
Walker, Gilbert Thomas      360 361
Walker, James      328 331 333 537 544
Wallenburg, G.      94
Waring, E.      503
Watson, G.N.      11 105 125 158 226 231 249 268 355 444 483 485 513 519 566 575
Wave-motions, equation of, general solutions      125
Wave-motions, equation of, generalised to p dimensions      128
Wave-motions, equation of, used to obtain addition theorems for Bessel functions      129
Waves on water, and the method of stationary phase      229
Waves, electric      56 226 446
Webb, H.A.      351 523 533 536
Weber's (H. F.) function $E_{\nu} (z)$       308
Weber's (H. F.) function $E_{\nu} (z)$ with large argument and order, asymptotic expansion of      316
Weber's (H. F.) function $E_{\nu} (z)$ with large argument, asymptotic expansion of      313
Weber's (H. F.) function $E_{\nu} (z)$ , connexion with Anger's function      310
Weber's (H. F.) function $E_{\nu} (z)$ , connexion with Struve's function      336
Weber's (H. F.) function $E_{\nu} (z)$ , differential equation, satisfied by      312
Weber's (H. F.) function $E_{\nu} (z)$ , integrals expressed in terms of      312
Weber's (H. F.) function $E_{\nu} (z)$ , recurrence formulae for      311
Weber's (H. F.) function $E_{\nu} (z)$ , representation of Airy's integral (generalised) by      321
Weber's (H. F.) function $E_{\nu} (z)$ , tables of      see “Struve's function”
Weber's (H. F.) function $E_{\nu} (z)$ , Theisinger's integral for      338
Weber's (H.) discontinuous factor      405
Weber's (H.) infinite integrals      391 393 395 396
Weber's (H.) infinite integrals, discontinuous types of      398 402 405 406 408 411
Weber, Heinrich      63 64 67 75 165 167 195 196 210 211 212 386 391 392 393 394 395 396 398 402 405 406 408 421 450 451 452 453 454 455 468 469 470 495
Weber, Heinrich Friedrich      308 309 310 311 312 315 320
Weierstrass, C.T.W.      358
Weierstrassian products, expression for Bessel functions as      497
Wendt, Caecilie      363
Weyl, H.      189 454
Weyr, E.      93 94
Whewell, W.      479
Whipple's transformation of Legendre functions      387
Whipple, F.J.W.      177 313 387
Whitehead, C.S.      81 82 132 148 203

1 2 3 4 5

О проекте