Determinants and Their Applications in Mathematical Physics

374 Index

determinants (continued)

centrosymmetric, 85

circulants, 79

continuants, 201

definition, 3

derivative, 15

equivalent, 212

expansion

Cauchy, 46

Laplace, 25

simple, 13

factors

centrosymmetric, 85

circulants, 79

skew-symmetric, 67

symmetric Toeplitz, 87

Fredholm, 240

Hankel, 104

Hessenberg, 90

Hilbert, 123

hybrid, 37, 55

Laplace expansion, 25

Matsuno, 192

nondistinct, 211

notation, vi

persymmetric, 105

product of two, three, 5, 33, 34

recurrent, 91

simple expansion, 13

skew-centrosymmetric, 90

skew-symmetric, 65

symmetric, 64

symmetric Toeplitz, 87

Toeplitz, 87

Turanian, 109

value identically 9, 15, 98, 260,

262

value identically 1, 83

Vandermonde, 52

Wronskian, 271, 280

Yamazaki–Hori, 232

determinants containing blocks of

zero elements, 30

determinants whose elements are

Appell polynomials, 115, 119

binomial and factorial numbers,

142

differences, 106

other determinants, 227, 230

prime numbers, 232

differences, 328

double-sum relations, 34, 112

Ehlers, 339

equations

Appell, 314

Benjamin–Ono, 241, 281

Dale, 236, 246

Einstein, 241, 287

Ernst, 241, 245, 302

Kadomtsev–Petviashvili, 240, 277

Kay–Moses, 237, 249

Korteweg–de Vries, 239, 263

Matsukidaira–Satsuma, 239, 258

Milne–Thomson, 256

Toda, 237, 252

Ernst, 241, 287, 302

Euler’s theorem on homogeneous

functions, 330

expansion

Cauchy, 46

Laplace, 25

of cofactors, 20

Factors

centrosymmetric, 85

circulants, 79

skew-symmetric, 67

symmetric Toeplitz, 87

Fiedler, 214

Freeman, 240

Frost and Sackfield, 173

Gradner, Greene, Kruskal, and

Miura, 240

generalized geometric series, 172,

323

generalized hyperbolic functions, 81

generating functions, 321, 322

Geronimus, 153

Grassmann, 1, 25

gravitational fields, 235

Hilbert, 123, 241

Hildebrand, 318

Hirota, 169, 240, 244, 295

homogeneous functions, 108, 330

Hori, 116, 129, 135, 244