Page 15 - Determinants and Their Applications in Mathematical Physics
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xiv Contents
6.10.2 Preparatory Lemmas ................. 287
6.10.3 The Intermediate Solutions .............. 292
6.10.4 Preparatory Theorems ................ 295
6.10.5 Physically Significant Solutions ........... 299
6.10.6 The Ernst Equation .................. 302
6.11 The Relativistic Toda Equation — A Brief Note ...... 302
A 304
A.1 Miscellaneous Functions .................... 304
A.2 Permutations .......................... 307
A.3 Multiple-Sum Identities .................... 311
A.4 Appell Polynomials ...................... 314
A.5 Orthogonal Polynomials .................... 321
A.6 The Generalized Geometric Series and Eulerian
Polynomials ........................... 323
A.7 Symmetric Polynomials .................... 326
A.8 Differences ........................... 328
A.9 The Euler and Modified Euler Theorems on Homogeneous
Functions ............................ 330
√
A.10 Formulas Related to the Function (x + 1+ x ) .... 332
2 2n
A.11 Solutions of a Pair of Coupled Equations .......... 335
A.12 B¨acklund Transformations .................. 337
A.13 Muir and Metzler, A Treatise on the Theory of
Determinants .......................... 341
Bibliography 343
Index 373
