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| L Sirovich — Techniques of Asymptotic Analysis With 23 Illustrations |
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| Предметный указатель |
Airy’s equations 127 191 289 293
Airy’s functions 126 174
Airy’s integrals 126 134 171 174
Airy’s integrals, relation to transition points 293
Airy’s integrals, Stoke’s lines of 133 134
Analytic continuations 3 68 129
Analytic continuations, of functions defined by an integral 38 39
Analytic continuations, of Laplace transforms 69
Asymptotic developments 4 7
Asymptotic developments, error estimates 25 60
Asymptotic developments, extended sense 10 11
Asymptotic developments, general 8
Asymptotic developments, in the sense of Poincare 9
Asymptotic developments, uniqueness 10 12 13
Asymptotic expansions 11 24 26
Asymptotic expansions, of Airy’s integrals 132 133 288 293
Asymptotic expansions, of Bessel functions 126 288
Asymptotic expansions, of Bromwich integrals 182 186
Asymptotic expansions, of Fourier integrals 74 181
Asymptotic expansions, of Laplace integrals 66 71 72 78 274
Asymptotic integration 17 19
Asymptotic power series 2
Asymptotic power series, derivative of 18 21
Asymptotic power series, uniqueness 12
Asymptotic sequences 7
Bellman, R. 300
Bessel functions 9 122 126 170
Bessel functions, asymptotic expansions of 126
Bessel functions, reduction to Airy’s function 171
Bessel’s equations 287
Biccati’s equation 190
Bleistein, N., l 40 170 171
Borel sum 35
Bromwich integral 182 186
Bromwich path 183
Carrier, G. 300
Cauchy integral formula 23 210
Cauchy sequence 207
Cayley — Hamilton theorem 208
Chako, N. 140
Characteristic polynomial of a matrix 209
Chester 171 173
Circuit relation 230
Classical adjoint of a matrix 193 209
Coddington, E. 188 300
Cofactor matrix 193
Cole, J. 300
Connection formulas for transition points 294 298
Convolution integrals 157
Copson, E. T. 300
Critical points 88 93 137 147
de Bruijn, N. 300
Derivatives of APS 18 21
Dieudonne, J. 10 44 300
Dispersive wave 102
Dominant solution 270 295
Dunford — Taylor integral 210 217 235 238
EDGE 270
Eigenvalues 201
Eigenvalues, degenerate 204 265
Eigenvalues, multiplicity of 202 225 235 242
Eigenvectors 201
Eigenvectors, generalized 239 242 244 246
Erdelyi, A. 10 76 79 300
Error estimate of AD 25 60
Error functions, complementary 73 161
Essential singularities 3 229 232 258 260
Euler transformation 29 33
Euler’s constant 177
Euler’s method 29
Existence of solution for ODE 188
Exponential function of a matrix 215 216
Focke, J. 137 140
Fourier integrals 62 71 88 157 163 181
Fr benius, method of 255
Friedman, B. 171 173
Friedrichs, K. 0 178 300
Frohman 299
Fuch’s theorem 232 241 255
Fuch’s type, equation of 258
Functions of matrices 207 209 211
Fundamental matrix solution 196 200 230 269 271
Fundamental system of solutions 196
Gamma function 25
Gauge Functions 8 9 17 18
Gel’fand, I. M. 139
Group velocity 102
Halmos, P. 192
Hamburger equation 288
Handelsman, R. 140 178
Hankel function 73 122
Heading, J. C. 299
Heaviside function 168
Hermitian matrix 1935 203
Hilbert transform 182
Huo, Wei-chi C. 104
Hypergeometric equation 257 258
Hypergeometric functions 159
Ince, E. L. 283
Indefinite integrals, asymptotic evaluation of 14
Indicial equation 256 257
Integral representations of Airy’s function 126
Integral representations of Bessel functions 126
Integral representations of Gamma functions 25
Integral representations of Hankel functions 73 122
| Integration by parts 40 164
Irregular singular point 230 234 259 278
Jeffrys, H. 300
Jones, D. S. 140
Jordan canonical form 204
Keller, J. 299
Kelvin’s formula 86 87 101 104
Kelvin’s formula, generalized 100
Kelvin’s formula, multidimensional integral 136
Kline, M. 140
Krook, M. 300
Landau symbols 5 6 7
Langer, E. 296
Laplace integrals 66 71 72 80 88 114 274
Laplace transforms 62 70 77 80 176 182 184
Laplace’s formula 80 83 96 164
Laplace’s method 80 272
Laurent expansions 286
Lauwerier, H. 299
Level curves 106
Levinson, B. 188 300
Lew, J. 178
Lynn, R. 299
Magnus 122 160 166
Matrix 192 195 201
Matrix solutions, fundamental 196 230 269 271
Matrix, adjoint of 193
Matrix, canonical forms 204
Matrix, characteristic polynomials 202 209 214
Matrix, classical adjoint of 193
Matrix, cofactor 193
Matrix, diagonal 202
Matrix, function of 207 211
Matrix, hermitian 193 203
Matrix, inner products 192
Matrix, Jordan canonical form of 204
Matrix, minimal polynomials 212
Matrix, normal 1933 203
Matrix, norms of 205 206
Matrix, null space of 194
Matrix, ranks 194
Matrix, similarity 203 230
Matrix, trace 198
Minimal polynomials 212 214
Multiplicity of eigenvalues 202 225
Neutralizers 753 88 93 138 140 142
Newton’s polygon 280
Normal matrix 193
Normal solution 271
Null space 191
Oberhettinger, F. 122 160 166
Olver, F. W. F. 27 296
Orthogonal transformations 141 144 230
Parabolic cylinder equation 191
Parabolic cylinder function 160 161 166
Pearson, C. 300
Poincare, H. 13
Polynomials, characteristic 202 209
Polynomials, minimal 212
Ranks of matrices 194
Recessive Solutions 270
Regular singular points 230 234 254 283
Riemann notation 258
Riemann — Lebesgue theorem 63
Riemann — Lebesgue theorem, generalized 64
Ritt’s theorem 36
Saddle points 105 113 117 126
Saddle points, coalescing of 171
Saddle points, formula 105 121 126
Saddle points, formula for complex large parameter 115
Saddle points, hills of 113
Saddle points, valleys of 113 174
Saddle, monkey 115 171
Scaler ordinary differential equations 234 254 278 285
Scaler ordinary differential equations, definition of irregular singular points 278
Scaler ordinary differential equations, definition of regular singular points 234 254 257 278
Shanks, D. 35
Shearing transform 240
Shilov, G. 139
Singular points of ODE 226 232
Singular points of ODE, irregular 230 234 259 278
Singular points of ODE, regular 230 234 254 257 273 276
Sirovich, L. 104 162
Soni, E. 122 160 166
Stationary phase, method of 86
Stationary phase, path 106
Stationary point 87 99 100
Steepest descent, method of 105
Steepest descent, path 106 107 108
Stirling’s formula 84
Stokes lines 3 60 73 133 134 270 275
Subdominant solution 270
Subnormal solution 271
Taylor’s Theorem 4
Transition point 292 297 298 299
Turning point 297
Uniform asymptotic expansion 164-175 296
Uniqueness of solution for ODE 188 189
Ursell 171 173
van der Corput 75
Variation of parameter method 200
Wasow, W. 289 300
Watson’s lemma 65 66 70
Wilcox, C. H. 27
WKB method 126 291 292 296 299
wronskian 197
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