Ex Libris                        Wanted                           
blank

       
blank

blank
blank
blank
blank
Olver F.W.J. Asymptotics and Special Functions
Olver F.W.J.  Asymptotics and Special Functions









?
Ctrl+Enter


: Asymptotics and Special Functions

: Olver F.W.J.

:

A classic reference, intended for graduate students, mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool.


: en

: // , /

:

ed2k: ed2k stats

: 1974

: 572

: 26.03.2005

: | | ID
blank
$R_1$, $R_2$, $R_{\infty}$ arcs      147
Abel Plana formula      290
Abel, N. H.      4
Abels identity      142
Abels theorem on continuity of power series      26
Airey, J. R.      72 536 543
Airy functions      53 393
Airy functions, asymptotic expansions of      103 105 116118 392394 413414
Airy functions, auxiliary functions for complex arguments      415416
Airy functions, auxiliary functions for real arguments      394397 404 433
Airy functions, bounds for      116117 394
Airy functions, differential equations for      55
Airy functions, graphs      393
Airy functions, history      433
Airy functions, integrals of      342344 394 430432
Airy functions, relation to Bessel functions      61 392 393
Airy functions, Wronskians      393 416
Airy functions, zeros      403405 414416
Airy integral      see Airy functions
Airy, G. B.      433
Airys equation      55
Airys equation, connection formula for solutions      55 507
Airys equation, inhomogeneous form      430432
Airys equation, numerically satisfactory solutions      278 393 414
Aitkens $\delta^2$-transformation      543
Alternating function      68 70
Anger function      84 103
Anger function of large order      84 103 336 352360
Annular sector      7
Anti-Stokes lines      504 518
Apostol, T. M.      144 152 219
Askey, R. A.      446
Associated Legendre equation      169 185 463 Legendre
Associated Legendre equation, connection formulas for solutions      171 179 490491
Associated Legendre equation, numerically satisfactory solutions      172173 178
Associated Legendre functions      see Legendre functions
Asymptotic approximations      see Asymptotic expansions Asymptotic
Asymptotic behavior of power series on circle of convergence      26 304306
Asymptotic expansions      4 16 Asymptotics Differential
Asymptotic expansions by integration by parts      6670 7579 106112 342343
Asymptotic expansions in complete sense of Watson      543
Asymptotic expansions of integrals      see Bleisteins method Haars Laplaces Method Friedman and Method Method Watsons
Asymptotic expansions of sequences      309310 (see also Asymptotic expansions of
Asymptotic expansions of sums      284292 295309
Asymptotic expansions to N terms      17
Asymptotic expansions with logarithmic singularities      322325 338339
Asymptotic expansions with nearly coincident saddle points and branch points      344346 361
Asymptotic expansions with nearly coincident saddle points and poles      346 361
Asymptotic expansions with two nearly coincident saddle points      351 352 357
Asymptotic expansions, compound      118
Asymptotic expansions, convergence of      1819
Asymptotic expansions, differentiation with respect to parameters      324
Asymptotic expansions, failure of      7679
Asymptotic expansions, functions with prescribed      2224 2930
Asymptotic expansions, fundamental properties      1619
Asymptotic expansions, generalized      2427 30 117118 313
Asymptotic expansions, history      34 2930 543544
Asymptotic expansions, implied constants      17
Asymptotic expansions, induction of expansions      71
Asymptotic expansions, neglect of exponentially small terms      78 95 105
Asymptotic expansions, nonuniqueness of sum      1718
Asymptotic expansions, numerical use of      105 519521 543544
Asymptotic expansions, operations with      1922
Asymptotic expansions, Poincares definition      4 1617 2425 105 543
Asymptotic expansions, transformation of      540544
Asymptotic expansions, uniqueness property      17
asymptotic relations      411 29
Asymptotic scale      25
Asymptotic sequence      25
Asymptotic solutions of differential equations      see Differential equations
Asymptotic sum      23
Asymptotic variable      17
Asymptotics      27
Asymptotics, paradox in      313
Bachmann, P.      4
Bakhoom, N. G.      84
Balogh, C. B.      382 425
Barnes, E. W.      104 301 321
Bateman Manuscript Project (B.M.P.)      64 188 189 277
Berg, L.      29 329 361
Bernoulli numbers      281284 291
Bernoulli polynomials      281284 321
Bernoulli polynomials, relation to Zeta function      283 292
Bertocchi, L.      479
Bessel functions      55 57 242 Hankel Modified
Bessel functions of first, second, and third kinds      242
Bessel functions of half-odd-integer order      59 241 244
Bessel functions of imaginary argument      60
Bessel functions of large argument      130133 242 269 317318
Bessel functions of large complex order      434
Bessel functions of large positive order      133134 334336 360 382 419426
Bessel functions, analytic continuation      57 244
Bessel functions, ascending series      57 243
Bessel functions, auxiliary functions for      436438 453457
Bessel functions, Bessels integral      55
Bessel functions, bounds for      59
Bessel functions, collected properties      435436
Bessel functions, connection formulas      238 239 242244
Bessel functions, derivatives with respect to order      243 244
Bessel functions, differential equations for      57 341
Bessel functions, generating function      56
Bessel functions, graphs      242 243
Bessel functions, history      277 278
Bessel functions, integral representations      5556 58 59 244 340
Bessel functions, integrals of      59 60 244 277 278
Bessel functions, Kapteyns inequality      426
Bessel functions, Mehler Sonine integrals      244
Bessel functions, Neumanns addition theorem      59
Bessel functions, Nicholsons integral      340
Bessel functions, Poissons integral      59 241
Bessel functions, recurrence relations      5859 436
Bessel functions, relation to confluent hypergeometric functions      255
Bessel functions, Schlaflis integrals      58
Bessel functions, sums of squares of      340342
Bessel functions, Wronskian      244
Bessel functions, zeros      214 244250 278 408 426 434
Bessels equation      57 (see also Modified Bessel equation)
Bessels equation, inhomogeneous form      274 432
Bessels equation, numerically satisfactory solutions      242243 278
beta function      37 38
Birkhoff, G. D.      391 517
Bleistein, N.      104 105 332 345 361
Bleisteins method      344351 361
Boin, P. W. M.      105
Born approximation      451
Borsch Supan, W.      320
Bound states      497501
Boundary value problem      197
Bounded variation      27
Boyer, T. R      434
Braaksma, B. L. J.      321
Brillouin, L.      228
British Association for the Advancement of Science (B.A.)      134 376 405 433 526
Bromwich, T. J. Ia.      2 21 29 54
Buchholz, H.      278
Burkhardt, H.      105
Calogero, F.      210 479
Caratheodory, C      189
Carleman, T.      29
Carlini, F.      228
Cauchy principal value      41 72 346
Cauchy, A. L.      4
Chako, N.      105
Chakravarti, P. C      321
Chebyshev polynomials      52 185
Cherry, T. M.      223 433 544
Chester, C      351 361
Chester, Friedman, and Ursells method      see Method of Chester Friedman and
Chowla, S.      336
Chuhrukidze, N. K.      479
Cirulis, T.      105 361
Clark, R. A.      434
Clausen, Th.      169
Clemmow, P. C      361 .
Cochran, J. A.      251 381 434
Cohn, J. H. E.      228
col      see Saddle point
Compact set      24
Completely monotonic function      68
Conditionally convergent integrals      74
Confluent hypergeometric equation      254 (see also Whittakers equation)
Confluent hypergeometric equation with exponents differing by integer      259
Confluent hypergeometric equation, asymptotic solutions      256
Confluent hypergeometric equation, connection formulas for solutions      257259
Confluent hypergeometric equation, numerically satisfactory solutions      259
Confluent hypergeometric functions      255 256 Whittaker
Confluent hypergeometric functions as functions of parameters      255
Confluent hypergeometric functions of large argument      256258
Confluent hypergeometric functions, Barnes integral      302
Confluent hypergeometric functions, converging factor for      531536
Confluent hypergeometric functions, history      277 278
Confluent hypergeometric functions, integral representations      255257 302
Confluent hypergeometric functions, recurrence relations      256 259
Confluent hypergeometric functions, Rummers transformations      256 257
Confluent hypergeometric functions, Wronskians      255 259
Conical functions      473 474
Connection formulas      166 228 480
Connection formulas at singularity      480490
Connection formulas for simple turning points      483 491494 503506 510513
Connection formulas for three turning points      516
Connection formulas for two turning points      494503 513516
Connection formulas, central      517
Connection formulas, history      516517
Connection formulas, lateral      517
Connection formulas, stretching-matching method      517
Connection formulas, vanishing of error terms      508510
contour      29
Convergently beginning series      3
Converging factor      522 543
Coppel, W. A.      202
Copson, E. T.      22 31 64 116 123 137 138 156 334
Cosine integrals      4243
Cosine integrals, asymptotic expansion of      67 320
Cosine integrals, Laplace transform of      43
Critical points, method of      see Method of stationary phase
Curtis, A. R.      232
Cylinder functions      248 (see also Bessel functions)
Darboux, M. G.      310
Darbouxs method      309310 321
Darbouxs method, examples      311315
Davis, P. J.      26 30 64
Dawsons integral      44
Dawsons integral, converging factors for      531 544
De Bruijn, N. G.      9 11 29 138 321 329
de Kok, F.      105
Debye, P.      134 137 382
Deleted neighborhood      18
Dieudonne, J.      29 105
Difference operator      299 537
Differential equations      see Connection formulas Irregular LG Singularities Turning-point
Differential equations for products of solutions      169
Differential equations with parameter      see Connection formulas Differential with LG Singularities Turning-point
Differential equations with parameter, admissible cases      474479
Differential equations with parameter, asymptotic solutions      203206 208211 224 371373 382386
Differential equations with parameter, atypical cases      477 478
Differential equations with parameter, basic equation      475
Differential equations with parameter, basic functions      475 479
Differential equations with parameter, behavior of coefficients in asymptotic solutions      365 368371 386
Differential equations with parameter, classification of cases      362 474
Differential equations with parameter, condition solutions are functions of single variable      475 479
Differential equations with parameter, continuity of solutions      143 145
Differential equations with parameter, eigensolutions      214 216
Differential equations with parameter, eigenvalues      214217 228 494501
Differential equations with parameter, error bounds for asymptotic solutions      203204 209 366 385
Differential equations with parameter, formal series solutions      364366 383 477
Differential equations with parameter, history      189 228 391
Differential equations with parameter, holomorphicity of solutions      144 146 236
Differential equations with parameter, inhomogeneous      386388
Differential equations with parameter, zeros of solutions      211214
Differential equations with simple pole      see Singularities of differential equations
Differential equations with simple pole, asymptotic solutions for complex variables      460462 478479
Differential equations with simple pole, asymptotic solutions for real variables      208211 447451 478479
Differential equations with simple pole, coefficients in asymptotic solutions      445 448 462463
Differential equations with simple pole, connection formulas      483490
Differential equations with simple pole, error bounds for asymptotic solutions      440446 457460
Differential equations with simple pole, formal series solutions      438440
Differential equations with simple pole, history      478 479
Differential equations with simple pole, inhomogeneous      479
Differential equations with simple pole, zeros of solutions      451453
Differential equations with three regular singularities      156
Differential equations, Cauchys method for existence theorems      148 149
Differential equations, Cayleys identity      193
Differential equations, dominant solutions      155 199
Differential equations, existence theorems for complex variables      145148 189
Differential equations, existence theorems for real variables      139143 189
Differential equations, exponential-type solutions      190
Differential equations, fundamental solutions      141142 146
Differential equations, identification of solutions      155
Differential equations, inhomogeneous      143 270274 386388 429430
Differential equations, linear independence of solutions      142 146 154
Differential equations, local behavior of solutions      190
Differential equations, method of successive approximations      141 233
Differential equations, normal series      230
Differential equations, normal solution      230
Differential equations, numerically satisfactory solutions      154155 223 431432
Differential equations, ordinary point      148 153
Differential equations, oscillatory solutions      190
Differential equations, Picards method for existence theorems      141
Differential equations, recessive solution      155 199
Differential equations, subdominant solution      155
Differential equations, subnormal solution      231
Differential equations, trigonometric-type solutions      190
Differential equations, zeros of solutions      211214 405408 451453
Digamma function      39
Dingle, R. B.      517 543
Discontinuities      73
Distinguished point      7 25
Doetsch, G.      104 112 317 323
Domain      29
Dominated Convergence Theorem      54
Doming, J. J. 317      
Duncan, C. E.      321
eigenvalue problems      214217 228 494501
Elliptic integrals      161
Energy-conservation equation      503
Entire functions, asymptotic expansions for large arguments      307309 321
Erdelyi, A.      25 30 44 81 86 104 105 115 120 228 276 278 325 361 391 412 433 446
Error function      4344 64
Error function, asymptotic expansion of      67 112
Error function, complementary      43
Error function, converging factors for      526527 544
Error function, relation to incomplete Gamma functions      45
Error term      2
Error test      6869
Error-control function      194 222 399
Error-control function, variation at singularity      200202 401
Euler Maclaurin formula      281 284285
Euler Maclaurin formula, applications      285289 292295
Euler Maclaurin formula, contour integral for remainder term      289292
Euler Maclaurin formula, error bounds for      285
Euler Maclaurin formula, evaluation of constant term      287 292
Euler Maclaurin formula, generalized      284
Euler Maclaurin formula, history      321
Euler, L.      3 63 161
Eulers constant      34 40 64 292
Eulers transformation      537
Eulers transformation, applied to asymptotic expansions      540543
Evgrafov, M. A.      83 306 315 321 517
Exponential integral      4041 64
Exponential integral with Eulers transformation      540543
1 2 3
blank
blank
blank
HR
@Mail.ru
       © , 2004-2017
   | Valid HTML 4.01! | Valid CSS!