Author: Victor Kowalenko

The Stokes Phenomenon, Borel Summation and Mellin-Barnes Regularisation

eBook: US $74 Special Offer (PDF + Printed Copy): US $156
Printed Copy: US $119
Library License: US $296
ISBN: 978-1-60805-097-0 (Print)
ISBN: 978-1-60805-010-9 (Online)
Year of Publication: 2009
DOI: 10.2174/97816080501091090101

Introduction

The Stokes phenomenon refers to the emergence of jump discontinuities in asymptotic expansions at specific rays in the complex plane. This book presents a radical theory for the phenomenon by introducing the concept of regularization. Two methods of regularization, Borel summation and Mellin-Barnes regularization, are used to derive general expressions for the regularized values of asymptotic expansions throughout the complex plane. Though different, both yield identical values, which, where possible, agree with the original functions. Consequently, asymptotics has been elevated to a true discipline yielding precise solutions. All researchers, who seek asymptotic solutions to problems, will find this a most valuable book.

Foreword

- Pp. iii-iv (2)
John P. Boyd
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Preface

- Pp. v-xi (7)
Victor Kowalenko
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Introduction

- Pp. 1-6 (6)
Victor Kowalenko
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Stokes’s First Example

- Pp. 7-12 (6)
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Dingle’s Rules and Theory of Terminants

- Pp. 13-21 (9)
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Regularisation

- Pp. 22-46 (25)
Victor Kowalenko
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Asymptotics for the Error Function

- Pp. 47-63 (17)
Victor Kowalenko
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Contemporary Views of the Stokes Phenomenon

- Pp. 64-81 (18)
Victor Kowalenko
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Mellin-Barnes Regularisation

- Pp. 82-113 (32)
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Numerics of MB-Regularised Forms

- Pp. 114-132 (19)
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Generalised Terminants

- Pp. 133-153 (21)
Victor Kowalenko
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Borel Summation of Generalised Termi-nants

- Pp. 154-192 (39)
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Extension of Borel Summation

- Pp. 193-223 (31)
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Conclusion

- Pp. 224-236 (13)
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Appendix

- Pp. 237-238 (2)
Victor Kowalenko
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References

- Pp. 239-243 (5)
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Author Index

- Pp. 244
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Subject Index

- Pp. 245-249 (5)
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