Higher Special Functions
A Theory of the Central Two-Point Connection Problem Based on a Singularity Approach
Series: Encyclopedia of Mathematics and its Applications; 188;
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Product details:
- Publisher Cambridge University Press
- Date of Publication 23 May 2024
- ISBN 9781009123198
- Binding Hardback
- No. of pages316 pages
- Size 240x165x23 mm
- Weight 626 g
- Language English 556
Categories
Short description:
This detailed reference explores the theory of differential equations, developing efficient methods for finding higher special functions.
MoreLong description:
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 Jaff&&&233;, who laid the foundation with the calculation of the quantum mechanical energy levels of the hydrogen molecule ion.
'This comprehensive treatise builds the theory of second-order linear ordinary differential equations in terms of the zeros of their leading coefficient. Beyond the functions of hypergeometric class is relatively unexplored territory: the 'higher special functions'. Lay's approach is deeply scholarly, and grounded in applications to dislocations and quantum theory.' Michael Berry, University of Bristol
Table of Contents:
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 Jaff&&&233;; References; Index.
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