xiv Contents
6.10.2 Preparatory Lemmas ................. 2876.10.3 The Intermediate Solutions.............. 2926.10.4 Preparatory Theorems ................ 2956.10.5 Physically Significant Solutions ........... 2996.10.6 The Ernst Equation.................. 3026.11 The Relativistic Toda Equation — A Brief Note...... 302A 304
A.1 Miscellaneous Functions.................... 304A.2 Permutations .......................... 307A.3 Multiple-Sum Identities .................... 311A.4 Appell Polynomials ...................... 314A.5 Orthogonal Polynomials.................... 321A.6 The Generalized Geometric Series and EulerianPolynomials........................... 323A.7 Symmetric Polynomials .................... 326A.8 Differences ........................... 328A.9 The Euler and Modified Euler Theorems on HomogeneousFunctions ............................ 330A.10 Formulas Related to the Function (x+√
1+x
2
)
2 n
.... 332A.11 Solutions of a Pair of Coupled Equations.......... 335A.12 B ̈acklund Transformations .................. 337A.13 Muir and Metzler, A Treatise on the Theory ofDeterminants.......................... 341Bibliography 343
Index 373