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| Hille E. — Ordinary Differential Equations in the complex domain |
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| Предметный указатель |
Matuda, T. 469
Maximum: modulus 31
Maximum: principle of 30
MCTA (Methods in Classical and Functional Analysis) 39
Mean: square modulus 129
Mean: value 30
Mellin, Hjalmat: integrals 256
Mellin, Hjalmat: transform 274—280 282
Miller, John Boris 281
Minimal equation 244
Minkowsky, Hermann 3
Minorant 63—67
Mittag — Leffler, Goesta 16
Mittag — Leffler, Goesta, star 192
Modular: function 263 395
Modular: group 395
Modulo (up to multiples of) 146
Modulus: maximum 31
Modulus: mean square 129
Modulus: of a Jacobi elliptic function 263 430
Modulus: of a Jacobi elliptic function, complementary 430
Moebius, August Ferdinand: function 115
Moebius, August Ferdinand: linear fractional function 19 212
Molk, J. 465
Multiplication: matrix 8
Multiplication: matrix, left right: by a matrix 394
Multiplication: matrix, left right: commutator 344
Multiplication: matrix, left right: spectra 345
Multiplication: scalar 2
Nagumo, Mitio: inequality 13 16
Nagumo, Mitio: uniqueness theorem 13
Negative 2
Nehari, Zeev 288 300
Nehari, Zeev, number of zeros in disk 303 306 320
Nehari, Zeev, Schwarzion and univalence 320 391 401
Neighborhood 4 18
Neighborhood infinitudinal 414
Neighborhood polar 132 139
Neumann Carl 213
Neumann, F. 210
Nevanlinna, Frithiof 61
Nevanlinna, Roll 61
Nevanlinna, Roll, abstract of theory 114—129
Nevanlinna, Roll, characteristic function 117
Nevanlinna, Roll, enumerative function 116 124
Nevanlinna, Roll, fundamental theorems 117 125
Nevanlinna, Roll, fundamental theorems, partial converse 391 401
Nevanlinna, Roll, proximity function 116
Newton, Sir Isaac: diagram 94
Newton, Sir Isaac: fluxional equations 41
Newton, Sir Isaac: indeterminate coefficients 41
Newton, Sir Isaac: trial and error 47
Noerlund, Niels Erik: difference equations 279—280 282
Norm 4
Norm, of matrix 8
Normal: bi 111
Normal: principal 111
Normal: series 362
Normal: type of meromorphic function 118
Noshiro, Kiyoshi 142
Oberhetyinger, F. Bateman papers 248 468
Okubo, K.A. 370 373
Optimization of majorant 39
Order(ing): Archimedean 3
Order(ing): of branch point 79
Order(ing): of DE 41
Order(ing): of elliptic function 424 428
Order(ing): of entire function 119
Order(ing): of meromorphic function 119
Order(ing): of zeros of ww' 268—269
Order(ing): partial 2
Order(ing): partial, proper 2
Order(ing): partial, reflexive 2
Order(ing): partial, transitive 2
Order(ing): solution 162
Orientation 195 329
Osgood, William Fogg 377
Packing, closest 133
Painlevie, Paul 76 79 87 102 439—440 465 469
Painlevie, Paul, theorem on: algebraic branch points 83—85
Painlevie, Paul, theorem on: determinateness 87—90
Painlevie, Paul, theorem on: infinitary solutions 85—87
Painlevie, Paul, transcendent 438—44
Painlevie, Paul, transcendents, asymptotics (Boutroux) 444—448
Papperitz, Erwin: uniformization of hypergeometric functions by modular functions 394—401
Parallelogram: law 20
Parallelogram: period 427
Parameter: analytic dependence on 73—74
Parameter: expansion in powers of a 74—75
Parameter: external 67
Parameter: initial 297
Parameter: interchange of argument and 259
Parameter: internal 67
Parameter: matrix 202
Parameter: matrix, Parameter: variation of 67—74 314—315
Parameter: matrix, transformation of 203
Part: imaginary 17
Part: principal 27
Part: real, 17
Peano, Guiseppe 71
Period: additive 154
Period: of elliptic functions 427 430
Period: of exponential functions 20
Period: parallelogram 427
Period: parallelogram, approximate 447
Perron, Oskar: order estimate 163 198 338 372
Phase portraits 456
Picard, Emile: genus theorem 127
Picard, Emile: method of successive approximations 47—51 75
Picard, Emile: second order nonlinear DE's with only fixed critical points 439 466
Picard, Emile: theorem 27 126 263
Picard, Emile: value 126
Plemelj, Josip: Riemann—Hilbert problem 201 357 372
Pochhammer, L.: Barnes notation 231
Poincare, Henri 35 53 97 102 355
Poincare, Henri, analysis situs 97
Poincare, Henri, asymptotic power series 52 57 223
Poincare, Henri, automorphic functions 128 263 378
Poincare, Henri, celestial mechanics 75 469
Poincare, Henri, countability of elements 35
Poincare, Henri, curves defined by DE's 97
Poincare, Henri, infinite determinants 244
Poincare, Henri, majorants 52
Poincare, Henri, noneuclidean geometry 388
Poincare, Henri, phase portraits 456
Point: at infinity 18
Point: fixed 9
Point: singular 76
Point: star 314
Point: transcendental critical 79
Poisson, Simeon-Denis: equation 229 230 234
Pokarnyi, V.V. 300 306 391 401
Pole 27
Polynomial: Cebysev 387
Polynomial: Cebysev, minimax property 388
Polynomial: Hermite 231
Polynomial: Jacobi 387
Polynomial: Laguerre 227
Polynomial: Legendre 210 387
Poschl, Klaus: growth of solutions 165 198
Postulates: distance 3
Postulates: norm 4
Potential: logarithmic 19
Potential: Newtonian 245
Power: fractional 20
Power: type (rational by Boutroux) 87 413 415—416
Power: with matrix exponent 347
Principle: argument 29
Principle: maximum 28 30—31
Principle: permanence of functional equations 37
| Pringsheim, Alfred 23
Pringsheim, Alfred, theorem 23
Product: dot- = inner 8
Product: of linear transformations 6
Product: of matrices 8
Projection: idempotent 346
Projection: stereographic 18 118 394
Projectivity 141
Projectivity, relation 110
Property 1
Property, P of matrix 192
Pseudopole 250
psi series 249—253 405 408 454 459—468
psi series logarithmic 249 451 454 460—463
Puisseux, V.A.: method of 94 434
Quadratures 104 141
Quadrics, central confocal 247
Radius: associated radii 36
Radius: of convergence 21
Radius: of curvature 111
Radius: of torsion 111
Rainierse, Petms Joannes 466
Ramification: completely ramified value 126
Ramification: index 126
Ramification: total algebraic 126
Rank of irregular singularity 162
Rearrangement of power series: direct 22—23
Rearrangement of power series: repeated 34—35
Reciprocation 374
Reduction of order of DE 160
Region 18
Region, fundamental 378
Region, zero-free 292—300
Removal of first derivative 179
Representation: asymptotic 52 57 220—226 369
Representation: by double integrals 256—257
Representation: by double integrals, Euler transforms 258—265
Representation: by double integrals, Euler transforms, hypergeometric 265—270
Representation: by double integrals, Laplace transforms 270—274
Representation: by double integrals, Mellin and Mellin — Barnes transforms 274—280
Representation: by integrals 253—282
Representation: by psi series 249—253
Representation: Lappo — Danilevskij's, theorem 386
Representation: theorems 249—282
Residue(s) 28
Residue(s), calculus of 28 63
Residue(s), theorem 28—29
Resolution of the identity 346
Resolvent of: commutator 353
Resolvent of: matrix 346
Resultant 78
Riccati, Conto Jacopo 42 103
Riccati, Conto Jacopo, Acta Eruditorum 103
Riccati, Conto Jacopo, DE 89—90 103—143
Riccati, Conto Jacopo, geometric applications 110—114
Riccati, Conto Jacopo, Malmquist's theorem 129—138
Riccati, Conto Jacopo, Malmquist's theorem, generalizations 138—140 143
Riccati, Conto Jacopo, matrix, DE's 407—408
Riemann problem 43 356—360
Riemann problem, history 357 394
Riemann — Birkhoff problem 341
Riemann, Bernhard 17 24 200
Riemann, Bernhard, Cauchy, equations 19
Riemann, Bernhard, hypergeometric integrals 304
Riemann, Bernhard, lectures 394
Riemann, Bernhard, P-function 201
Riemann, Bernhard, problem 43 356—360 372 394
Riemann, Bernhard, Stieltjes integral 25
Riemann, Bernhard, Stieltjes integral, sums 25
Riemann, Bernhard, surface 20
Robertson, M.S. 401
Roots: characteristic 8
Roots: latent 8
Roots: nth 20
Roots: of trinomial equation 208
Rouche, Eugoene 186
Rouche, Eugoene, theorem 186
Rousseau, Jean-Jaques 1
Sansone, G. 432
Sario, Leo 142
Schaeffer, Juan Jorge 469
Schafheitlin, P. 283
Schlesinger, Ludwig 198 469
Schlesinger, Ludwig, algebraic hypergeometric functions 400
Schlesinger, Ludwig, Euler transform 258 281
Schlesinger, Ludwig, Laplace transform 281
Schlesinger, Ludwig, regular-singular points 338
Schlomilch, Otto 212 216
Schwarz, Binyamin 283 300 307 320
Schwarz, Hermann Amandus: differential invariant (Schwarzian) 374—401
Schwarz, Hermann Amandus: on algebraic hypergeometric functions, 383—388
Schwarz, Hermann Amandus: on conformat mapping 377—383
Schwarz, Hermann Amandus: symmetry principle 240 379 394
Schwarz, Hermann Amandus: triangular functions 385 395
Schwarzian 374—401
Schwarzian, applications to: algebraic solutions 383—388
Schwarzian, applications to: conformal mapping 377—383
Schwarzian, applications to: uniformization 394—400
Schwarzian, applications to: univalence 388—393
Schwarzian, derivative 110 374
Schwarzian, invariants of projectlye group 374—375
Schwarzian, invariants of projectlye group, Lavie 375
Schwarzian, Kummer 374 394
Schwarzian, Riemann 374 394
Scorza—Dragoni, Guiseppe 449
Separation of variables in Laplace-Poisson equations 229 230 234
Sequence, Cauchy 4
Series: asymptotic 52 57 223 362
Series: Baker 451 456
Series: binomial 363
Series: Coulson — March 450 466
Series: divergent 52
Series: factorial 3634
Series: Fourier power 120
Series: hypergeometric 201
Series: lacunary 23
Series: Laurent 26
Series: normal 362
Series: normal, subnormal 362
Series: power, 214
Series: psi 249—256
Serret, Alfred 111
Set 1
Set closed 4
Set open 4
Sheet 20
Shift of matrix parameters 368—369
Shimizu, Tatsujiro: spherical characteristic 118
Sine equation, asymptotic 183
Singularities: algebraic 34
Singularities: essential 27
Singularities: fixed, of DE 43 76—81
Singularities: irregular, of DE 144 147
Singularities: logarithmic 34
Singularities: matrix 8
Singularities: movable, of DE 43 76—81 86—87
Singularities: on circle of convergence 23
Singularities: pole 27
Singularities: regular, of DE 144 147 155—161 342—
Singularities: topological, of curve system 456
Skendzic, M. 466
Smith, Russell 433
Smith, Russell, autonomous polynomial systems 460—465
Smith, Russell, quadratic system, psi series 459
Solution: dependence on parameters 67—74
Solution: existence and uniqueness of 40—75
Solution: existence and uniqueness of, history 40—44
Solution: expansion in powers of a parameter 74
Solution: general 43
Solution: oscillatory 178 182
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