Higher Special Functions: A Theory of the Central Two-Point Connection Problem Based on a Singularity Approach [Hardcover]

This detailed reference explores the theory of differential equations, developing efficient methods for finding higher special functions.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.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 Jaff?, who laid the foundation with the calculation of the quantum mechanical energy levels of the hydrogen molecule ion.1. Introduction; 2. Singularities in action; 3. Fuchsian differential equations: the cornerstones; 4. Central two-point connection problems and higher slÓK