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| Ïîèñê ïî óêàçàòåëÿì |
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| Hille E. — Ordinary Differential Equations in the complex domain |
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| Ïðåäìåòíûé óêàçàòåëü |
Abel, Niels Henrik 52 151
Abel, Niels Henrik, elliptic functions 262
Abel, Niels Henrik, Wronskian 324
Abelian integrals 263
Aczel, Janos 39
Addition 2
Addition of matrices 8
Addition of operators 6
Addition, theorems for: elliptic functions 430—431
Addition, theorems for: tangent function 106
Adjoint 254
Adjoint, anti 254
Adjoint, self 254
Affinity 117
Ahlfors, Lars V. viii 61
Ahlfors, Lars V., characteristic function 118—119
Ahlfors, Lars V., Schwarzian and conformal mapping 391
Algebra 2
Algebra, Banach 6
Analysis situs (topology) 97
Analytic Function Theory 39
Anticlinal 289
Argument 17
Argument, interchange of, and parameter 254
Argument, principle of 29
Asymptotics: Boutroux 444—448
Asymptotics: in the plane 178—191
Asymptotics: on the real line 171—178
Asymptotics: on the real line, of cubic equation 178
Autonomous: equation 47 80
Autonomous: polynomial system 455—465
Baker, E.B.: series 451 466
Banach, Stefan 5
Banach, Stefan, algebra 6
Banach, Stefan, fixed point theorem 9
Banach, Stefan, space 5
Bank, Steven S. 143
Barnes, F. Ernest William 276
Barnes, F. Ernest William, integral for Bessel function 279
Barnes, F. Ernest William, integral for hypergeometric function 276—278
Barnes, F. Ernest William, Poohhammer – notation 221
Basis 6
Bateman papers see Erdelyi Magnus Oberhettinger and
Beesack, Paul R. 283 300—301 304 306—308 320 391
Bellman, Richard 468
Bendixson, Ivar 16 74
Bendixson, Ivar, theorem 16 39 70 74
Bernoulli: Daniel 41 103—104 212
Bernoulli: Jakob 41 104
Bernoulli: Johann 41 104
Bernoulli: Johann, equation 104
Bessel, Friedrich Wilhelm: equation 103 211—216 279 312—317
Bessel, Friedrich Wilhelm: equation, quasi 178
Bessel, Friedrich Wilhelm: functions, 1st kind 212
Bessel, Friedrich Wilhelm: functions, 2nd kind 213
Bessel, Friedrich Wilhelm: functions, 3rd kind (Hankel) 215
Bestimmtheitsstelle 147
bezout 78
Bezout, method 78
Bieberbach, Ludwig 198 360 400 468
Binormal 111
Birkhoff, George David 44 74
Birkhoff, George David generalized Laplace transform 271—274
Birkhoff, George David, canonical form 361 378
Birkhoff, George David, regular singular point 337—338 372
Birkhoff, George David, Riemann problem 201 357 370—372
Birkhoff, George David, second order linear DE 370—371 373
Bliss, Gilbert Ames 102
Bocher, Maxime 247 468
Bolzano, Bernhard: Weierstrass theorem 4
Boruvka, Otakar viii 468
Boundary: entrance 173
Boundary: natural 23
Boundary: natural, movable 434
Boundary: of domain d (D) 18
Bouquet, Jean-Claude 79 402
Bouquet, Jean-Claude 1st order equations singular at the origin 402—416
Bouquet, Jean-Claude, Brio- elliptic functions 79—80 102 418—428 431 435—439 468
Bourbaki, N. 468
Boutroux, Pierre 86 102 135 402 411 432—433 468
Boutroux, Pierre solutions, of exponential type 86 312
Boutroux, Pierre solutions, of exponential type, of power type 87 413 415—416
Boutroux, Pierre, asymptotics 283 319 444—448 468
Branch point: algebraic 34
Branch point: algebraic, movable 83—85
Branch point: logarithmic 77
Branch point: transcendental 76 79
Briot, Charles see Bouquet
Brouwer, L.E.J., fixed point theorem 9 44 74
Burmann, Hans-Wilhelm 279 282
Cacciopoli, R. 44 74
Calcul des limites 51 74
Calculus of residues 28—30
Calculus of residues, Lindeloef 83
Caratheodory, Constantin: condition 13
Caratheodory, Constantin: conformal mapping 377
Caratheodory, Constantin: uniqueness theorem 51
Cayley, Arthur: Hamilton – theorem 9
Cebysev, Pafnutij Livovic: polynomials 387—388
Cebysev, Pafnutij Livovic: polynomials, minimax property 388
Center = vortex 314
Cesari, Lamberto 468
Characteristic function: of R. Nevanlinna 117
Characteristic function: of rational function 118
Characteristic function: spherical of Shimizu and Ahlfors 118—119
Chazy, Jean 431 439 465
Clairaut, Alexis-Claude 41
Closure 4
Closure, relation 210
Coddington, Earl A. 198 371 468
Colombo, Serge 282
Commutator 344
Commutator, Daletzskij's formula 347 353
Commutator, Foguel's theorem 347
Commutator, resolvent 347 353
Commutator, spectrum 344
Comparison theorems 300—308
Component, maximal 132
Condition: Caratheodory 13
Condition: Lifpschitz 5
Cone: positive conal harmonics 211
Conformal Mapping: application of Schwarzian to 377—383
Conformal Mapping: by modular functions 397—398
Conformal Mapping: of circular polygons 378—383
Conjugacy 203
Conjugacy of complex numbers 20
Connectedness 18
Connectedness simple 20
Conti, R. 432 469
Continuation, analytic 33—38
Continuation, analytic of solution 81—96 192—194 327—333
Continuity 18
Contraction 9
Contraction, fixed point theorem 9—11
Convergence: absolute 21
Convergence: equi- 119—121
Convergence: exponent of 120
Convergence: holomorphy preserving 27—28
Convergence: in norm 99
Convergence: induced 27
Convergence: radius of 21
Convergence: uniform 27
Convexity: horizontal 286
Convexity: theorem 290—291
Convexity: vertical 286
Coordinates, confocal 245
Coppel, W.A. 194 199 328 425 466 468
Coulson, C.A. 450 466
Crelle, August Leopold, Journal 151
Curvature: radius of 111
| Curvature: vector 111
Cut 20
Cylinder functions: circular (= Bessel) 229—230
Cylinder functions: elliptic 234—242
Cylinder functions: parabolic 230—233
Daletzkij, Yu.L. 347 353 372
de Cauchy, Augustine-Louis, Baron 17 24 42 52
de Cauchy, Augustine-Louis, Baron, calcul des limites 51 74
de Cauchy, Augustine-Louis, Baron, extension 251
de Cauchy, Augustine-Louis, Baron, Hadamard formula 21
de Cauchy, Augustine-Louis, Baron, integral 24 31
de Cauchy, Augustine-Louis, Baron, kernel 22( see also Kernel)
de Cauchy, Augustine-Louis, Baron, majorant 57—60
de Cauchy, Augustine-Louis, Baron, Riemann equations 19
de Cauchy, Augustine-Louis, Baron, sequence 4
de Cauchy, Augustine-Louis, Baron, theorem 25
Defect 126
Defect, relation 126
Dependence: linear 2 151
Dependence: linear in- 2 151
Derivative 19
Determinant 7
Determinant infinite 248
Diameter, topological 4
Dicylinded 44
Difference equation 257 277 279 281
Difference equation, of Bessel functions 213 280
Difference equation, of Legendre functions 211 274
Difference set of spectrum 346 367
Differential equation = DE 40
Differential equation linear 144
Differential equation nonlinear 41
Differential equation nonlinear, order of 41
Differential equation, linear homogeneous 144
Differential equation, linear nonhomogeneous 145
Differential equation, linear self—adjoint 179 254
Differential equation, linear self—adjoint, anti 254
Differential equation, linear singular 328
Differential equation, solution 41
Differential equation, solution general 43
Differential equation, solution particular 43
Differential equation, solution singular 43
Differential equations, linear 144—373
Differential equations, linear, complex oscillation theory 283—320
Differential equations, linear, first order 144—148
Differential equations, linear, integral representation 253—283
Differential equations, linear, matrix DE 322—373
Differential equations, linear, nth order 321—373
Differential equations, linear, second order 148—153
Differential equations, linear, special second order 200—248
Differential equations, linear, special second order, Bessel 211—216 278 312—315
Differential equations, linear, special second order, Floquet 242—243
Differential equations, linear, special second order, Halre 247
Differential equations, linear, special second order, Hermite — Weber 228—238 315—317
Differential equations, linear, special second order, Hill 244
Differential equations, linear, special second order, hypergeometric 200—208 265—270 308—310 399—400
Differential equations, linear, special second order, hypergeometric confluent 226
Differential equations, linear, special second order, Laguerre 227
Differential equations, linear, special second order, Lamg 245—246
Differential equations, linear, special second order, Laplace 216—228
Differential equations, linear, special second order, Legendre 208—211 260—264 279—280 310—315
Differential equations, linear, special second order, Matbleu 234—242 317—318
Differential equations, linear, special second order, Titchmarsh 188—191 319
Differential equations, nonlinear 40—143 374—467
Differential equations, nonlinear, autonomous 1st order Briot — Bouquet 80 91—96 102 416—432
Differential equations, nonlinear, autonomous 2nd order Briot — Bouquet 435—439
Differential equations, nonlinear, autonomous polynomial systems 460—467
Differential equations, nonlinear, autonomous quadratic systems 455—460
Differential equations, nonlinear, Eraden and Thomas — Fermi Des 448—455
Differential equations, nonlinear, existence and uniqueness of solutions 40—75
Differential equations, nonlinear, first order Briot — Bouquet DEs singular at z = 0 402—416
Differential equations, nonlinear, Painleve transcendent 439—448
Differential equations, nonlinear, Painleve transcendents, asymptotics of Boutroux 444—448
Differential equations, nonlinear, Riccari DE's, generalizations 138—143
Differential equations, nonlinear, Riccati DE's 103—143
Differential equations, nonlinear, singularities 76—102
Differential forms, quadratic 211 233
Differential operators: linear L, L*, M, M* 254—256
Differential operators: v = z d/dz 203 276 321—322
DIMENSION 2
Discriminant equation 77
Disk(s): circular 18
Disk(s): circular, closest packing of 133—134
Distance 1
Distance chordal 18
Distance postulates 1
Domain 18
Domain, boundary of 18
Dominant 56 63—67 171—176
Dominant, sub- 171—177
Dot: Newton's symbol 97
Dot: product (= inner product) 9 114
Dulac, Henri 251 281 431—432 467—468
Eigenvalue 8
Elements 1
Elements algebraic 34
Elements infinitary 34
Elements logarithmic 392
Elements negative 2
Elements neutral 2
Elements regular 34
Elements zero 3
Elhptic functions 79 80 91 102 427—431
Elhptic functions of Jacobi 91 127 207 262
Elhptic functions of Weierstrass 96 126—127 143
Elhptic functions, DEs satisfied by 126—7 143 416—427 434—439
Emden, R.: equation 433 448—453 456 466
Emden, R.: Gaskugeln 448 466 468
Equation(s): Cauchy — Riemann 19
Equation(s): characteristic, of matrix 8
Equation(s): defining algebraic function 77
Equation(s): difference see Difference equation
Equation(s): differential see Differential equation; Differential equation linear; non-linear;
Equation(s): discriminant 77—78
Equation(s): indicial 157 344
Equation(s): Laplucian 19
Equation(s): matrices 101
Equation(s): minimal, of matrix 244 346
Equation(s): natural, of curve 118
Equation(s): paths 330
Equi-convergence 119 120 121
Esrdelyi, A.: Bateman papers 248 468
Euler, Leonard: Bessel's DE 212
Euler, Leonard: beta function 109 206 265
Euler, Leonard: DE 343
Euler, Leonard: Mascheroni constant 209
Euler, Leonard: transform 258—265
Euler, Leonard: transform hypergeometric 265—270
Euler, Leonard: transform, Legendre DE 260—261
Existence theorems 40—75
Existence theorems, concept of solutions 404
Existence theorems, dominants and minorants 63—67
Existence theorems, fixed point method 44—47
Existence theorems, indeterminate coefficients 41—51
Existence theorems, majorants 51—57
Existence theorems, majorants, calcul des limites 52
Existence theorems, majorants, Cauchy majorant 57—60
Existence theorems, majorants, Lindeloef majorant 60—63
Existence theorems, successive approximations 47—51
Existence theorems, successive approximations, Caratheodory condition 51
Existence theorems, variation of parameters 67—74
Exponential function 19
Exponential function of matrices 99
Exterior 195
Extremum 284
Fabry, Eugene: subnormal series 362 373
Fermi, Enrico 449
Fermi, Enrico, Thomas — Fermi equation 96 433 446—453
Field: complex 2
Field: definite vector 297
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