The Partition Method For A Power Series Expansion: Theory And Applications by Victor KowalenkoThe Partition Method For A Power Series Expansion: Theory And Applications by Victor Kowalenko

The Partition Method For A Power Series Expansion: Theory And Applications

byVictor Kowalenko

Hardcover | January 19, 2017

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The Partition Method for a Power Series Expansion: Theory and Applicationsexplores 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 numbers
  • Compares generating partitions via the BRCP algorithm with the standard lexicographic approaches
  • Describes how to program the partition method for a power series expansion and the BRCP algorithm
Dr Victor Kowalenko is a Senior Research Fellow in the Department of Mathematics and Statistics, University of Melbourne, Australia. Since 2009, he has been associated with the ARC Centre of Excellence in Mathematics and Statistics of Complex Systems. He began his research career by joining the DSTO's railgun project in Maribyrnong in ...
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Title:The Partition Method For A Power Series Expansion: Theory And ApplicationsFormat:HardcoverDimensions:322 pages, 9.41 × 7.24 × 0.98 inPublished:January 19, 2017Publisher:Academic PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0128044667

ISBN - 13:9780128044667

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Table of Contents

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