SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

Topic #4  ------------   OP-SF NET 7.5  -------------  September 15, 2000
From: OP-SF NET Editor 
Subject: New book on Special Functions

The following information is from the web site: 

Special Functions -  A Unified Theory Based on Singularities
Wolfgang Lay (Stuttgart) and  Sergei Yuryevitsh Slavyanov (St. Petersburg)
Oxford University Press,
320 pp.; 50 line illus; 0-19-850573-6, November 2000

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 the complex domain. The
number and characteristics of the singularities serve as a basis for
classification of each individual special function. Links between linear
special functions (as solutions of linear second-order equations), and
non-linear special functions (as solutions of Painleve equations) are
presented as a basic and new result. Many applications to different areas
of physics are shown and discussed. The book is written from a practical
point of view and will address all those scientists whose work involves
applications of mathematical methods. Lecturers, graduate students and
researchers will find this a useful text and reference work.

 1. Linear Second-order ODE with Polynomial Coefficients
 2. The Hypergeometric Class of Equations
 3. The Heun Class of Equations
 4. Application to Physical Sciences
 5. The Painleve Class of Equations
 A. Gamma-Function and Related Functions
 B. CTCPs for Heun Equations in General Form
 C. Multipole Matrix Elements
 D. SFTools - Database of the Special Functions

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