Higher Special Functions
A Theory of the Central Two-Point Connection Problem Based on a Singularity Approach
Seiten
2024
Cambridge University Press (Verlag)
978-1-009-12319-8 (ISBN)
Cambridge University Press (Verlag)
978-1-009-12319-8 (ISBN)
This detailed reference provides solutions for singular boundary eigenvalue problems of linear ordinary differential equations of second order. Containing new functions, unseen eigenvalue curves, a general method of solution, examples of unsolved problems and historical context, it will be indispensable for graduate students and researchers alike.
Higher special functions emerge from boundary eigenvalue problems of Fuchsian differential equations with more than three singularities. This detailed reference provides solutions for singular boundary eigenvalue problems of linear ordinary differential equations of second order, exploring previously unknown methods for finding higher special functions. Starting from the fact that it is the singularities of a differential equation that determine the local, as well as the global, behaviour of its solutions, the author develops methods that are both new and efficient and lead to functional relationships that were previously unknown. All the developments discussed are placed within their historical context, allowing the reader to trace the roots of the theory back through the work of many generations of great mathematicians. Particular attention is given to the work of George Cecil Jaffé, who laid the foundation with the calculation of the quantum mechanical energy levels of the hydrogen molecule ion.
Higher special functions emerge from boundary eigenvalue problems of Fuchsian differential equations with more than three singularities. This detailed reference provides solutions for singular boundary eigenvalue problems of linear ordinary differential equations of second order, exploring previously unknown methods for finding higher special functions. Starting from the fact that it is the singularities of a differential equation that determine the local, as well as the global, behaviour of its solutions, the author develops methods that are both new and efficient and lead to functional relationships that were previously unknown. All the developments discussed are placed within their historical context, allowing the reader to trace the roots of the theory back through the work of many generations of great mathematicians. Particular attention is given to the work of George Cecil Jaffé, who laid the foundation with the calculation of the quantum mechanical energy levels of the hydrogen molecule ion.
Wolfgang Lay is Privatdozent at the Universität Stuttgart and Actuary at the Allianz Group. His research focuses on special functions. He has spent time at the Universities of Oxford and Bristol and at the Euler International Mathematical Institute in St. Petersburg. He co-authored the book 'Special Functions: A Unified Theory based on Singularities' (2000) with S. Yu. Slavyanov.
1. Introduction; 2. Singularities in action; 3. Fuchsian differential equations: the cornerstones; 4. Central two-point connection problems and higher special functions; 5. Applications and examples; 6. Afterword; A. Standard central two-point connection problem; B. Curriculum vitae of George Cecil Jaffé; References; Index.
| Erscheinungsdatum | 18.10.2021 |
|---|---|
| Reihe/Serie | Encyclopedia of Mathematics and its Applications |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-009-12319-X / 100912319X |
| ISBN-13 | 978-1-009-12319-8 / 9781009123198 |
| Zustand | Neuware |
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