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

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

by Victor Kowalenko


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Product Details

ISBN-13: 9780128044667
Publisher: Elsevier Science
Publication date: 02/02/2017
Pages: 322
Product dimensions: 5.98(w) x 9.02(h) x 0.75(d)

About the Author

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 the early 1980’s before transferring to the DSTO facility at Fishermen’s Bend to work on aeronautical systems. He then returned to the Department of Physics, University of Melbourne as one of the inaugural Australian Research Fellows to work on particle-anti-particle plasmas and general relativistic magnetohydrodynamics. It was here that he introduced the partition method for a power expansion. Between 2001 and 2003, when he was a Senior Research Fellow in the School of Computer Science and Software Engineering, Monash University, he was able to develop the method further and to extend it to intractable problems in mathematics and physics.

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

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