The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more, including chapters on discrete orthogonal polynomials and elliptic functions. The authors show how a very large part of the subject traces back to two equations - the hypergeometric equation and the confluent hypergeometric equation - and describe the various ways in which these equations are canonical and special. Providing ready access to theory and formulas, this book serves as an ideal graduate-level textbook as well as a convenient reference.
Contains the various principal special functions in common use and their basic properties and manipulations.
When we look at Kummer's equation ( 7.4 ) we see that the Laguerre polynomial is a 1F1 - function : Ln ( x ) = ( " + a ) n 1F1 ( -n ; a + 1 ; v ) , where the binomial coefficient is chosen for normalization and on account of convention ...
The Russian mathematician views the theoretical and practical aspects of special functions and illustrates their significance in problem solving in physics and engineering
The subject of this book is the theory of special functions, not considered as a list of functions exhibiting a certain range of properties, but based on the unified study of singularities of second-order ordinary differential equations in ...
Physics, chemistry, and engineering undergraduates will benefit from this straightforward guide to special functions.
The subjects treated in this book have been especially chosen to represent a bridge connecting the content of a first course on the elementary theory of analytic functions with a rigorous treatment of some of the most important special ...
The Handbook of Special Functions provides in-depth coverage of special functions, which are used to help solve many of the most difficult problems in
This book contains contributions from the proceedings at The Fields Institute workshop on Special Functions, q-Series and Related Topics that was held in June 1995.
We believe that this is the first time that the theory of classical or thogonal polynomials of a discrete variable on both uniform and nonuniform lattices has been given such a coherent presentation, together with its various applications ...
Pages 292–316 of: XVIIth International Congress on Mathematical Physics. World Scientific. Bourbaki, N. 1968. Groupes et Alg`ebres de Lie. Chapitres IV, V et VI. Hermann, Paris. Also translated in English, Springer, 2002.