Determinants and Their Applications in Mathematical Physics

Index 375

Identities

Cauchy, 36

Cusick, 178

double-sum, 112

equivalent determinants, 212

Hirota operator, 221

hybrid determinant, 37, 55

Jacobi and variants, 38

matrix, 165, 233

Matsuno, 187

multiple-sum, 311

Vandermondian, 60, 63

integral equations

Fredholm, 240

Gelfand, Levitan, and

Marchenko, 236

Inverceanu, 84

Jacobi, v, 38

Kac, 237

Kajiwara, 169, 238

Karlin, 109, 153

Kaufman, 84

Kerr, 244

Kronecker delta function, 304

Kyriakopoulos, 244

Lamb, 240

Langmuirwaves, 238

Laplace, v

Laplace expansion, 25

lattice theory, 235

Laurent series, 335

Lawden, 153, 157, 165

Leibniz, v, 221

l’Hopital, 52

Littlewood, 187

Liu, 169

Matsuno, 187, 192, 241, 281

Milne–Thomson, 169, 238

Mina, 99

minors

complementary, 19

first, 12

rejecter and retainer, 18

second and higher, 19

Muir and Metzler, v, 78, 177, 341

Nakamura, A., 240

Nakamura, Y., 243, 245

Neugebauer, 244

Nimmo, 240

numbers

binomial and factorial, 212

complex, 79, 256

Eulerian, 325

prime, 232

Stirling, 217, 306, 324

v-, 137

Ohta, 169, 246

operations, row and column, 10

operators

associated with cofactors, 24

Hirota, 221

Pandres, 174

permutations, 307

Pfaffians, 73

Pipes, 84

plasma, 238

polynomials

Appell, 314

characteristic, 94

Euler and Eulerian, 157, 323

Hermite, 322

homogeneous, 112

identical, 212

Laguerre, 153, 321

Lawden, 157

Legendre, 154, 322

orthogonal, 153, 321

symmetric, 54, 326

P ̈oppe, 240

product of two, three determinants,

5, 33, 35

Reciprocal differences, 238

reciprocal power series, 92

recurrence relations, 264, 265, 321,

322

rejecter and retainer minors, 18

relativity theory, 235, 241

Rodrigues, 127, 154, 174, 321, 322,

323

R ̈osler, 174

row vectors, 7