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| Baker F — An Introduction to the theory of multiply periodic functions |
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| Предметный указатель |
 function, differential equations satisfied by 48 49 59
function, expressed algebraically 38
function, expression of squares of its differential coefficients 39
function, formulae for addition of half periods 102—104
function, of arguments u+v 132—138
function, of double arguments 120—124 129
function, the fundamental 97
Abel 263 327
Abel's theorem 176
Abel's Theorem, its converse 181
Addition of arguments for the p functions 132—138
Algebraic equations, Kronecker's analysis of 273
Algebraic functions, behaviour about any point 190
Analytical continuation, account of 214
Appell 204 285 329
Asymptotic directions of Kummer surface correspond to conjugate directions of Weddle surface, and conversely 127
Asymptotic lines of Kummer surface 113 151 162
Asymptotic lines of Steiner's quartic surface, and of its reciprocal cubic surface 151
Asymptotic lines of Weddle surface 125
Bateman 68 126 138 327
Birational transformation of Kummer surface 79 154
Birational transformation of Weddle surface 131
Blumenthal 329
Bolza 327 328
Brioschi 327 328
Burkhardt 328
Burnside 269 330
Canonical and normal systems of periods 2 263
Caspary 328
Castelnuovo 330
Cauchy 285
Cayley 68 150
Ciani 320
Clebsch 150 204
Collinear points of a Kummer surface 118
Complementary system of defective integrals 240
Complex linear, a particular 67
Complex multiplication, or principal transformation 245
Complex surface, Plucker's 158
Complexes, linear, associated with the Kummer surface 74
Complexes, linear, six in involution 168
Conjugate points on a Kummer surface 114
Construct, monogenic, meaning of 215
Continuation, analytical, account of 214
Corpus of algebraic functions 281
Correspondence, between a set of n points of a Riemann surface and a point of a surface in n dimensions 279
Correspondence, of points of Kummer and Weddle surface 39 65 76
Cousin 285
Cremona 150
Cross-ratio identity between theta functions and integrals of the third kind 35
Cubic surface with four nodes 139—150 152 153
Curve upon the Weddle surface with defective integrals 322
Curves of Kummer surface for which the surface integrals are single valued 320
Cycles of roots of an algebraic equation 177 190
Darboux 127 138 151 158
Defective integrals, in general 228
Defective integrals, the case of one integral reducing to an elliptic integral 250
Defining equation for general theta function 19
Determinant, invariant factors of 165
Determinant, the expansion of a 314
Differential equations satisfied by sigma functions 48
Differential equations satisfied by sigma functions, the general covariantive form of these equations 49—54
Dissection of a Riemann surface 2 263
Double argument, functions of 120—124 129
Dyck 263
Elementary factors of a determinant 165
Elementary integral of the third kind 5 9
Enriques 330
Expansion of the sigma functions 83
Expression of multiply-periodic functions by theta functions 283
Factorial integrals 318
Fricke 267 269
Frobenius 238 287 312 328 330
Gauss 267 329
Goepel tetrad of nodes 153
Gopel 153
Gordan 204
Group of a Riemann surface 255
Group of a septic curve in space 326
Group of a Weddle surface 131
Group of birational transformations of a Kummer surface 79—82
Hartogs 330
hermite 204 327 329
hilbert 273
Hudson 118 138 150 151 158 160 320 327
Humbert 144 150 155 328
Hurwitz 202 255 267 269 270 329
Hyperelliptic surface 155 321
Identical vanishing of theta function 33 96
Implicit-function theorem, Weierstrass's 187
Indeterminate parameters 198 273
Indetermination, points of 200
Index, the, in case of defective integrals 232
Infinitesimal periods 203
Infinity-construct, of a meromorphic function 201
Inflexional lines of Kummer surface 113
Inflexional lines of Steiner's quartic surface and its reciprocal 151
Inflexional lines of Weddle surface 125 127
Inflexional lines, principal asymptotic curves of Kummer surface 162 322
Integral functions of two variables, fundamental properties 17
Integrals of Kummer surface which are integrals of the first kind 320
Integrals of the first, second or third kind 2
Integrals, elementary integral of second kind deduced by differentiation from elementary integral of third kind 9
Interchange of argument and parameter for integral of third kind 8 11
Invariant factors of a determinant 165
Inversion problem for integrals of the first kind 29 246 250
jacobi 204 256
Jacobi's inversion problem 29
Jacobi's inversion problem, generalised 246 250
Jacobian functions, zeros of a simultaneous system 293
Jessop 151
JORDAN 164
Klein 118 138 151 267 269 320 327 328
Kowalevski 255 272
kronecker 203 204 267 273 285 298
Kronecker's method for algebraic equations 273
Kummer 320
Kummer matrix 56
Kummer surface: asymptotic or inflexional curves 113 162 322
Kummer surface: becoming a tetrahedroid 156
Kummer surface: birational transformation of 79—82
Kummer surface: correspondence with Weddle surface 39 65 76
Kummer surface: degenerating into a Plucker complex surface 158
Kummer surface: determined to pass through an arbitrary plane quartic curve 320
Kummer surface: finite (ambiguously signed) integrals upon 43
Kummer surface: finite integrals for the satellite of a point 78
Kummer surface: integrals of first kind of curves of 320
Kummer surface: irrational equation of 108 110 328
Kummer surface: its equation at length 41
| Kummer surface: its equation by a symmetrical determinant 41 59
Kummer surface: its singular points and planes deduced 60—65
Kummer surface: other finite integrals upon 115
Kummer surface: parametric expression of 38 40
Kummer surface: referred to a Goepel tetrahedron of nodes 153
Kummer surface: referred to a Rosenhain tetrahedron 153
Kummer surface: satellite point upon 75
Kummer surface: tangent section of 78 110 321 328
Kummer surface: the fundamental linear complexes and quadrics 79—82 320
Kummer surface: whose singular planes are tangent planes of original, having a singular conic common with this 136
Lacroix 329
Laguerre 150
laurent 329
legendre 256
Lie 118 127 151
Liiroth 330
Limiting points of an aggregate 212
Linear complexes 74 79 163
Linear transformation of periods 252
Linear transformation of periods, of functions 103
Linear transformation of periods, of Kummer surface 79
Logarithmic coefficients of an algebraic integral 4
Loria 150
Matrix notation, explanation of 12
Matrix, elementary factors and reduction of 165
Matrix, orthogonal, of bilinear forms 176
Matrix, orthogonal, of sigma functions 106
Matrix, reduction to diagonal form 303
Matrix, six in involution 168 320
Matrix, skew-symmetric, of integers 307
Matrix, the six fundamental for a Kummer surface 73 74 79
Meromorphic functions 202
Molk 276
Monogenic construct 215
Multiplication, complex 245 263 329
Multiplicity, the, in case of defective integrals 232 250
Natani 329
Normal and canonical systems of periods 2 263
Olbers 329
Orthogonal matrix of bilinear forms 175
Orthogonal matrix of sigma functions 106
Painleve 161
Parameter of a place on a Riemann surface 2 177
Parametric expression of Kummer and Weddle surface 39 77
Pascal 328
Periodic function in general 203
Periodic function in general, values assumed by upon a monogenic construct 219
Periods of elementary normal integrals 7
Periods of elementary normal integrals, relations between periods of integrals of first and second kind 14
Periods of elementary normal integrals, relations necessary for a general multiply-periodic function 224
Periods of elementary normal integrals, rule for half-periods obtained by integration between branch places on a Riemann surface 32
Picard 329
Plane section of a certain hyperelliptic surface 155
Plane section of Kummer surface 320
Pliicker 158
Pluecker's complex surface 158
Poincare 255 269 285 297 329
Power series in two variables 183
Power series in two variables, a set of simultaneously vanishing 192
Quadrics, the ten fundamental for a Kummer surface 81 320
Quartic curve of 168
Quartic curve of collineations 265
Quartic curve of of four concurrent bitangents 255
Quartic curve of, Kummer surface passing through an arbitrary 320
Quartic surface, Cayley's paper referred to 68
Quartic surface, Steiner's 139—150
Reduction of theory of general multiply-periodic function to theory of algebraic functions 199
Reichardt 118 139 151
Relations connecting periods of general multiply-periodic function 224
Relations connecting periods of integrals of first and second kind 14
Reye 68 138 150
Richmond 327
Riemann 203 204
Riemann surface, a set of n arbitrary places of birationally related to one place of a surface in n dimensions 279
Riemann surface, with defective elliptic integral is capable of birational self-transformation 255
Riemann surface, with defective integrals 231
Rohn 138 328
Rosenhain 153
Rosenhain tetrahedron 153
Salmon 320
Satellite point upon a Kummer, or Weddle surface 75 114
Schottky 152 327
Schroter 150
Segre 151
Series for the sigma functions 83
Sigma function, expansion of 83
Sigma function, expression of  100
Sigma function, expression of  101. See also Theta function
Sigma function, the fundamental 97
Simart 329
Steiner 139
Sylvester 134 141 285
Tangent section of Kummer surface 76 110 321 328
Tetrahedroid 157
Theta function, a general, number and sum of zeros 234 235
Theta function, arising in connexion with multiply-periodic function 228
Theta function, general, denning equation for 19. See also Sigma function
Theta function, identical vanishing of 33 96
Theta function, of first order, fundamental identities 23
Theta function, of the second order 98 108
Theta function, upon a Riemann surface, number and position of zeros 27
Transformation of Riemann surface 255 279
Transformation of Weddle and Kummer surface 65 76
Transformation of Weddle surface 131
Transformation, birational, of Kummer surface 79 154
Transformation, of periods 237 252
Transformation, principal, or complex multiplication 245 263 329
Triply-periodic functions 161
Twin points upon a Kummer surface 114 117
Vahlen 276
Variability of an analytic function 218
Weber 263 269
Weddle matrix 65
Weddle surface, asymptotic lines of 125
Weddle surface, birational transformation of 131 326
Weddle surface, construction for tangent plane of 68
Weddle surface, correspondence with Kummer surface 39 65 76
Weddle surface, curve of contact of tangent cone from node upon 322
Weddle surface, elementary properties of 66 67
Weddle surface, fundamental equation for projection from a node 72
Weddle surface, its equation at length 71 78
Weddle surface, parametric expression of 38 40 77
Weierstrass 150 198 203 272 327 328 329
Wiltheiss 328
Wirtinger 245 283 285 297 298 318 329
Zero construct of meromorphic function 201
Zeros of simultaneous system of vanishing Jacobian functions 293
Zeros of theta function upon a Riemann surface 27
Zeta function expressed by integrals of the second kind 37
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