Higher Special Functions: A Theory of the Central Two-Point Connection Problem Based on a Singularity...

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Wolfgang Lay (Universität Stuttgart)

Higher Special Functions

A Theory of the Central Two-Point Connection Problem Based on a Singularity Approach

Wolfgang Lay (Universität Stuttgart)

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English

Cambridge University Press
23 May 2024

Real analysis, real variables; Complex analysis, complex variables; Differential calculus & equations

Series: Encyclopedia of Mathematics and its Applications

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.

By: Wolfgang Lay (Universität Stuttgart)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 240mm, Width: 165mm, Spine: 23mm
Weight: 626g
ISBN: 9781009123198
ISBN 10: 100912319X
Series: Encyclopedia of Mathematics and its Applications
Pages: 316
Publication Date: 23 May 2024
Audience: General/trade , ELT Advanced
Format: Hardback
Publisher's Status: Active

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.

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.

Reviews for Higher Special Functions: A Theory of the Central Two-Point Connection Problem Based on a Singularity Approach

'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