The Partition Method for a Power Series Expansion: Theory and Applications

The Partition Method for a Power Series Expansion: Theory and Applications explores how the method known as 'the partition method for a power series expansion', which was developed by the author, can be applied to a host of previously intractable problems in mathematics and physics.

In particular, this book describes how the method can be used to determine the Bernoulli, cosecant, and reciprocal logarithm numbers, which appear as the coefficients of the resulting power series expansions, then also extending the method to more complicated situations where the coefficients become polynomials or mathematical functions. From these examples, a general theory for the method is presented, which enables a programming methodology to be established.

Finally, the programming techniques of previous chapters are used to derive power series expansions for complex generating functions arising in the theory of partitions and in lattice models of statistical mechanics.

Explains the partition method by presenting elementary applications involving the Bernoulli, cosecant, and reciprocal logarithm numbersCompares generating partitions via the BRCP algorithm with the standard lexicographic approachesDescribes how to program the partition method for a power series expansion and the BRCP algorithm

1. Introduction 2. More Advanced Applications 3. Generating Partitions 4. General Theory 5. Programming the Partition Method for a Power Series Expansion 6. Operator Approach 7. Classes of Partitions 8. The Partition-Number Generating Function and Its Inverted Form 9. Generalization of the Partition-Number Generating Function 10. Conclusions Appendix A. Regularization Appendix B. Computer Programs