Page 389 - Determinants and Their Applications in Mathematical Physics

374 Index

determinants (continued) prime numbers, 232
centrosymmetric, 85 differences, 328
circulants, 79 double-sum relations, 34, 112
continuants, 201
definition, 3 Ehlers, 339
derivative, 15 equations
equivalent, 212 Appell, 314
expansion Benjamin–Ono, 241, 281
Cauchy, 46 Dale, 236, 246
Laplace, 25 Einstein, 241, 287
simple, 13 Ernst, 241, 245, 302
factors Kadomtsev–Petviashvili, 240, 277
centrosymmetric, 85 Kay–Moses, 237, 249
circulants, 79 Korteweg–de Vries, 239, 263
skew-symmetric, 67 Matsukidaira–Satsuma, 239, 258
symmetric Toeplitz, 87 Milne–Thomson, 256
Fredholm, 240 Toda, 237, 252
Hankel, 104 Ernst, 241, 287, 302
Hessenberg, 90 Euler’s theorem on homogeneous
Hilbert, 123 functions, 330
hybrid, 37, 55 expansion
Laplace expansion, 25 Cauchy, 46
Matsuno, 192 Laplace, 25
nondistinct, 211 of cofactors, 20
notation, vi
persymmetric, 105 Factors
product of two, three, 5, 33, 34 centrosymmetric, 85
recurrent, 91 circulants, 79
simple expansion, 13 skew-symmetric, 67
skew-centrosymmetric, 90 symmetric Toeplitz, 87
skew-symmetric, 65 Fiedler, 214
symmetric, 64 Freeman, 240
symmetric Toeplitz, 87 Frost and Sackfield, 173
Toeplitz, 87
Turanian, 109 Gradner, Greene, Kruskal, and
value identically 9, 15, 98, 260, Miura, 240
262 generalized geometric series, 172,
value identically 1, 83 323
Vandermonde, 52 generalized hyperbolic functions, 81
Wronskian, 271, 280 generating functions, 321, 322
Yamazaki–Hori, 232 Geronimus, 153
determinants containing blocks of Grassmann, 1, 25
zero elements, 30 gravitational fields, 235
determinants whose elements are
Appell polynomials, 115, 119 Hilbert, 123, 241
binomial and factorial numbers, Hildebrand, 318
142 Hirota, 169, 240, 244, 295
differences, 106 homogeneous functions, 108, 330
other determinants, 227, 230 Hori, 116, 129, 135, 244