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Iwasaki Katsunon, Kimura H., Shimomura S. — From Gauss to Painleve: A Modern Theory of Special Functions
Iwasaki Katsunon, Kimura H., Shimomura S. — From Gauss to Painleve: A Modern Theory of Special Functions



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Название: From Gauss to Painleve: A Modern Theory of Special Functions

Авторы: Iwasaki Katsunon, Kimura H., Shimomura S.

Язык: en

Рубрика: Математика/Справочники/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 347

Добавлена в каталог: 29.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\alpha$-times differentiation      47
$\tau$-function      226 227
$\varphi$-function      29
Affine bundle      136 140 241
Algebraic differential equation      120
Apparent singularity      123 152
Appell — Lauricella hypergeometric equation      246
Barnes integral      52 66 71 110
beta function      53 108
Cauchy's existence theorem      1
Cauchy's theorem (function theory)      97
Characteristic equation      6
Characteristic exponent      6
Circuit matrix      77
Completely integrable      23
Conjugacy class      76 80 89
conjugate      76
Connection matrix      77
Connection problem      52 77 96 111 114
Contiguity relation      42 45 47 54 73
D-irreducible      148
D-reducible      148
Deformation equation      158 190
Difference equation      27 66 72
Differential system      136
Double loop      60 61
Essential singular point      121 124
Euler integral      52 61 65 73 101
Euler operator      30
Euler transform      47 55 60 61 62
Exponent (of a function)      55
Exponent (of an equation)      6
Exterior algebra      15
Fifth Painleve equation      119 318
Finite part of a divergent integral      56
Fixed singular point of $P_J$      124 290 318
Formal transformation      263
Free group      78 79 104
Frobenius theorem      13
Frobenius's method      4
Fuchs relation      11 28 29 84 86
Fuchsian differential equation      9 10 27 28 77 148 149 151
Fundamental 2-form      18 193
Fundamental group      75 78 101 103
Fundamental solution      155
Fundamental system of solutions      2
Garnier system      119 172 195 202 204 207 211 230 232 234 235
Gauss hypergeometric differential equation      27 30
Gauss — Euler formula      75
Gauss — Kummer identity      73
Generalized hypergeometric equation      27
Groebner basis      46
Group of symmetries      127 128 230
Hamiltonian      18
Hamiltonian of $\mathcal{G}_n$      178
Hamiltonian of $\mathcal{H}_J$      142
Hamiltonian of $\mathcal{H}_n$      218
Hamiltonian system      17 18
Hamiltonian system $\mathcal{G}_n$      172
Hamiltonian system $\mathcal{H}_J$      141 142
Hamiltonian system $\mathcal{H}_n$      217
Hypergeometric differential equation      27 30
Hypergeometric differential operator      44
Hypergeometric Euler transform      62
Hypergeometric function      35 246
Hypergeometric function of Lauricella      251
Hypergeometric series      31 246
Hypergeometric type      62 73
Ideal (of a ring of differential operators)      46
Ideal (of an exterior algebra)      15
Indicial equation      6
Integrability condition      13 15 21
Integrable      12 15
Integral representation      52
Interpolation method      66
Inverse Mellin transform      71
Irreducible      79
Ising model      123
Jacobi identity      17
Jordan — Pochhammer equation      65
Kummer's 24 solutions      38 39
Landau's symbol      32
Laplace sequence      50
Lauricella hypergeometric differential equation      249
Lauricella hypergeometric function      251
Lauricella hypergeometric series      246
Lie algebra      17 27
Linear differential equation      1 16
Logarithmic singular point      9 87 92
M-invariant      154 155
Mellin transform      66 71
monodromy      75 77
Monodromy group      76 101 109 114 116
Monodromy preserving deformation      119 155 196
Monodromy representation      76 101 109 114 116
Movable branch point      121
Movable essential singular point      121 124
Non-logarithmic singular point      8 92
Normal form      290
Okubo type      73
Painleve      Preface
Painleve equation      119 122 123 126 141 257 290 318
Painleve property      121 195 207
Painleve system      141 172 226
Particular solution of $P_J$      145 146
Particular solution of $\mathcal{H}_n$      252
Particular solution of the Toda equation      48
Pfaffian system      12 15
Poincare's condition      257 279
Poisson bracket      17 172
Rational differential equation      120
Reducible      79 80
Regular singular      2
Riccati equation      121 253
Riemann datum      151
Riemann equation      28 79 84 85 89
Riemann P-function      29
Riemann scheme      11 28 36 84 169
Riemann surface      150
Riemann — Hilbert problem      151
Riemann — Liouville integral      54 59
Schlesinger system      196 202 204 211 227
Schlesinger type      195
Schur's lemma      150
Singular point of irregular type      257
Singular point of regular type      257 259 290 318
Sixth Painleve equation      119 318
SL-equation      166
SL-type      166
Step-down operator      43 46 49
Step-up operator      43 46 49
Stirling formula      31 71
Symmetries of      235
Symmetries of $P_{VI}$      128
Symmetries of $\mathcal{G}_n$      232
Symmetry      126
Symplectic 2-form      18 193
Symplectic transformation      19
Third Painleve equation      119 318
Toda equation      48
uniform      154
Weierstrass $\varphi$ function      121
wronskian      166
Wronskian matrix      163 278
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