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| Hille E. — Ordinary Differential Equations in the complex domain |
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| Предметный указатель |
Field: real 2
Fixed point 9
Fixed point, theorems: Banach 9
Fixed point, theorems: Brouwer 9
Fixed point, Volterra 11
Fixed point, Volterra, applied to Des 44—47
Fixed point, Volterra, applied to functional inequalities 14—16
Floquet, Gaston: theorem 245 248
Fluxion: al equations 41
Foguel, R.S.: theorem 347 372
Forms: indeterminate 96—102
Forms: quadratic differential 211 233
Forsyth, A.R.: zero-free region 284—285 320 468
Fourier, Joseph: coefficients 214 241
Fourier, Joseph: Legendre coefficients 210
Fourier, Joseph: ring 262
Fourier, Joseph: Theorie analytique de la chaleur 212
Fowler, R.H. 456 466
Fredholm, Ivar 16
Frenet, Jean-Frederic: formulas 111—113
Friedland, S. 391
Frobenius, Georg 147 342 344 349 352
Fuchs, Lazarus 76 147—148 263 342 344 355 439
Fuchs, Lazarus, Bestimmthetsstelle 147
Fuchs, Lazarus, fonctions Fuchsiennes 263
Fuchs, Lazarus, fundamental system 148
Fuchs, Lazarus, Fundamentalgleichu rig, determinierende 344
Fuchs, Lazarus, indicial equation 157 344
Fuchs, R. 439 440 465
Fuchsian class 147 353—360
Function(s): algebraic 32 77—78 102 383—388
Function(s): analytic 34
Function(s): automorphic 128 263
Function(s): Bessel 211—216 278 312—315
Function(s): beta 189 200
Function(s): branch of 34
Function(s): characteristic see Characteristic function
Function(s): confluent hypergeometric 226
Function(s): cylinder- see Cylinder functions
Function(s): elliptic see Elliptic functions
Function(s): entire 32
Function(s): exponential 19
Function(s): exponential, of matrices 99
Function(s): fractional linear = Moebius 19
Function(s): gamma, reciprocal 222
Function(s): gamma, reciprocal, of matrices 366—367
Function(s): generating of: Bessel functions 213
Function(s): generating of: Hermite polynomials 231
Function(s): generating of: Laguerre polynomials 227
Function(s): generating of: Legendre polynomials 210
Functional 325
Functional equation 37
Functional inequalities 12—17
Functional multiplicative 325
G-net 298
Gamma function: Hankel's integral 222 366
Gamma function: logarithmic derivative of 209
Gamma function: reciprocal 222
Gamma function: reciprocal, of matrices 366—367
Gammbier, B. 439 441 465
Gantmacher, F.R. 361 373
Garnier, R. 439 465
Garnier, R., Riemenn — Hilbert problem 372
Gaskugeln 448 466
Gauss, Carl Friedrich 200—201 211
Gauss, Carl Friedrich, hypergeometric series 201
Generators: of group 196
Generators: rectilinear 113
Genus = deficiency 127
Genus = deficiency, Picard's — theorem 127—128
Genus = deficiency, Picard's — theorem, elliptic case 127
Genus = deficiency, Picard's — theorem, hyperelliptic case 128
Geometry: of numbers 3
Geometry: of solutions of Des 97
Gol’dberg, A.A. 140 142
Grade of singularity 162 341
Green, George: formula 255
Green, George: transform 286—292
Gronwall, Thomas Hakvin: area theorem 389 393
Gronwall, Thomas Hakvin: lemma 15—16 39
Group: anharmonic 202
Group: anharmonic, conjugate element 203
Group: generators 330
Group: generators, finitely generated 196 330
Group: isomorphic 332
Group: modular 395
Group: monodromic 192—198 330—333
Group: motions in the plane 383
Group: projective 374
Group: rotations of the sphere 384
Group: rotations of the sphere, cyclic 383
Group: rotations of the sphere, dihedral 383
Group: rotations of the sphere, icosahedral 383
Group: rotations of the sphere, octahedral 383
Group: rotations of the sphere, tetrahedral 384
Growth: estimates of 31—32 162—170 333—343
Growth: exponential 411
Growth: for approach to singularity 333—342
Growth: in vertical strip 335
Growth: Liouville's theorem 32
Growth: power type 413—418
Growth: properties 420—426
Growth: v. Koch — Perron theorem 163—164 198 333—341 372
Gudermann, Christoffer 63 430
Hadamard, Jacques 21
Hadamard, Jacques, Cauchy- formula 21
Hadamard, Jacques, Cauchy- formula, extension 251
Hadamard, Jacques, entire functions of finite order 138
Hadamard, Jacques, version of Cauchy's integral 114 120
Harmonic 21
Harmonics: conical 211
Harmonics: solutions of kaplace's equation 21
Harmonics: spheroidal 211
Hartman, Philip 469
Hayman, W.K. 469
Heine, E.H.: Borel theorem 211
Heine, E.H.: Kegelfunktionen 211
Helson, Henry 372
Hermite, Charles 231
Hermite, Charles, polynomials 231
Hermite, Charles, Weber DE 228—233 315—317
Hiebert, David: Riemann problem 201 357
Hijkuhara, M. 432 469
Hilb, Emil 469
Hill, G.W.: equation 244
Hill, G.W.: infinite determinants 244 248
Hille, Einar 38—39 188 308 318 320 372
Hille, Einar, psi series 249—253 281
Hille, Einar, zeros of Hermite — Weber and Mathieu functions 248
Hochstadt, Harry viii 140
Holomorphic 17
Holomorphic f(a,b,c) 205—206 269
Holomorphic hypergeometric 200—208 260—270 276—280 309—311 383—388 394—401
Holomorphic meromorphic 32
Holomorphic modular 263 394—401
Holomorphic potential 19
Holomorphic rational 32
Holomorphic theta 263—265
Holomorphic theta, null 265
Holomorphic transcendental 32
Holomorphic value distribution 114—129
Horn angles 362—363
Horn, Jakob 251 281 363 373 469
Hsu, Ih-Ching viii 140
Hurwitz, Adolph 283—4 309 312 320
Hyperboloid 114
Hypothesis F 180
Idempotent 242 367
Identity Theorem 28
Implicit function theorem 63 75
| Ince, E.L. 248 281 320 371 465 469
Index = winding number 196
Indicatrices 289
Inequality: functional 12—17
Inequality: functional, categorical = determiserly 12
Integral: elliptic 262 267
Integral: hyperelliptic 264
Integral: integrator 25
Integral: inteland 25
Integral: line 24
Integral: Riemann — Stieltjes 25
Interior 18 195
Isochrone 41
Jacobi, Carl Gustav Jacob 394
Jacobi, Carl Gustav Jacob, elliptic functions 63 91 127 262
Jacobi, Carl Gustav Jacob, theta functions 263—265
Jacobson, N.: buffer condition 345
Jacobson, N.: prime ring 345
Jensen, J.L.V.W.: formula 114 116
Jordan, Camille: curve theorem 195 329
Julia, Gaston 148
Kamke, E. 200 248 281 469
Karamata, Jovan 466
Kellogg, Oliver Dimon 44
Kernel: Cauchy 25—26
Kernel: Cauchy, representation by Bessel functions 215—216
Kernel: Cauchy, representation by Legendre functions 210
Kernel: of integral equation 11
Kernel: of integral transform 255
Kimura, T. 432 469
Klein, Felix 247
Klein, Felix, automorphic functions 263
Klein, Felix, automorphic functions, fonctions kleiniennes 263
Klein, Felix, hypergcometric functions 461
Klein, Felix, hypergcometric functions, uniformization of 395 401
Koch, Helge von 16
Koch, Helge von, infinite determinants 244—245 248
Koch, Helge von, order estimate 163 198 338—341 372
Laguerre, Edmond: generating function 227
Laguerre, Edmond: polynomials 227
Laine, Ilpo 140 142
Lame, Gabriel: Des 245—246
Lame, Gabriel: with doubly periodic solution 246
Landau, Edmund 31
Laplace — Birkhoff transform 365—371
Laplace, Pierre-Simon: DE 216—223
Laplace, Pierre-Simon: integral 217
Laplace, Pierre-Simon: partial DE 19
Laplace, Pierre-Simon: Theorie analytiquc des probabilities 216 281
Laplace, Pierre-Simon: transform 270—278 217
Laplace, Pierre-Simon: transformation 228
Laplacian 19
Laplacian, change of variables in 228
Lappo Danilevskij, J.A. 344 469
Lappo Danilevskij, J.A., representation theorem 356 372
Lappo Danilevskij, J.A., Riemann problem 356—360 373
Laurent, Pierre-Alphons: series 26
Lavie, Metra 375 401
Lavoine, J. 282
Law, parallelogram 20
Legendre, Adrien-Mari: elliptic integrals 262
Legendre, Adrien-Mari: equation 208—211 260—264 310—311
Legendre, Adrien-Mari: polynomials 208—211
Leifschetz, Solomon 102 456 466 469
Levinson, Norman 198 371 469
Liapoonov, Alexander Mikailovie 338
Lie, Marius Sopbus 112
Lie, Marius Sopbus, Frenet formulas 111—112
Liebniz, Gottfried Wilhelm 42 104
Lipschitz, Rudolf 5
Lipschitz, Rudolf, Bessel functions 212
Lipschitz, Rudolf, condition 5
Lobatcevskij, Nikolai Ivanovi: geometry 385
Locus: of inflection 291—292
Locus: of tangency 300
LODE (Lectures on Ordinary Differential Equations) 39
Logarithm 20
Logarithm hyper 355
Logarithm, estimate of proximity function 123
Logarithm, estimate thereof 123
Logarithm, logarithmic derivative of gamma function 209
Logarithm, logarithmic derivative of meromorphic function 123
Logarithm, of regular matrix 244 247
Loop: double 197 219
Loop: double simple 218
Lotka, A.J. 455 466
Magnus, W.: Bateman papers 248 268
Mahler, Kurt 456
Majorant 52
Majorant, methods 51—57
Majorant, methods Cauchy's 57—60
Majorant, methods Lindeloef's 60—63
Malmquist, Johannes 16 103
Malmquist, Johannes, Briot — Bouquet DE 405 432
Malmquist, Johannes, theorem 113 129—137 143
Malmquist, Johannes, theorem, generalizations 138—143 417
Mambriani, A. 449 466
Mapping 5
Mapping bounded 5
Mapping conformal 377—383 365—367 395—396
Mapping onto (= surjection) 15
Mapping, order preserving 14
March, N.H. 450 466
Maric, V. 466
Masani, P. 361
Massera, J.L. 469
Matell, Mogens 169 198
Mathieu, Emile 234
Mathieu, Emile, equation 234—242
Mathieu, Emile, functions 236
Mathieu, Emile, functions, associated 336
Mathieu, Emile, functions, boundary value problem 235—238
Matrix differential equation 193
Matrix differential equation hypergeometric 202—203
Matrix differential equation of resolvent 408
Matrix differential equation Riccati 407—408
Matrix differential equation, first order in  322—371
Matrix differential equation, fundamental solution of 327
Matrix differential equation, fundamental solution of, analytic continuation 326—328
Matrix differential equation, fundamental solution of, monodromic group 126—128 330—333
Matrix differential equation, fundamental solution of, Wronskian 150—151 324—328
Matrix differential equation, vector 163
Matrix differential equation, with periodic coefficient matrix 243—244
Matrix(ces) 7
Matrix(ces), algebraic operations on 8
Matrix(ces), analytic functions of 243 347
Matrix(ces), analytic functions of, exponential functions of 99
Matrix(ces), analytic functions of, logarithm 244 247
Matrix(ces), analytic functions of, power 347
Matrix(ces), characteristic equation 8 98 346
Matrix(ces), characteristic values 8
Matrix(ces), characteristic vector 8
Matrix(ces), equivalent 99
Matrix(ces), Hamilton — Cayley theorem 9
Matrix(ces), idempotent 346
Matrix(ces), inverse 8 197
Matrix(ces), minimal equation of 244 346
Matrix(ces), nilpotent 197
Matrix(ces), norm of 8
Matrix(ces), norm of, of linear transformation in  7
Matrix(ces), similar 152
Matrix(ces), singular 8
Matrix(ces), space 8
Matrix(ces), spectrum 8
Matrix(ces), trace 324
Matrix(ces), transit 152 196
Matrix(ces), unit 99
Matrix(ces),property P 192
Matrix(ces),regular 8
Matrix(ces),resolvent of 346
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