Preface
Special functions arise in many applications of physics, mathematics, chemistry,
and engineering. When writing such a book, one is faced with numerous decisions,
such as: Which special functions and topics should be included? and What should
be assumed about the readers’ prior knowledge? This book is not elementary. The
reader should have a background in mathematics, physics, and programming with
MATLAB. 1
This book deals with computational methods for evaluating special functions
in the real and complex domains. MATLAB was used as programming language.
MATLAB is established at many universities, research institutes, and in industry. The
book comes with an additional toolbox called SPECFUNPHYS toolbox, extending
MATLAB’s capabilities with respect to special functions. The book covers more than
170 special functions mostly in the complex domain, which are either not covered
by standard MATLAB or in standard MATLAB restricted to the real domain.
The presentation of the special functions is organized in 23 chapters, each related
to a family of special functions together with examples or applications. Each chapter
starts with a brief introduction and an overview of the related SPECFUNPHYS
toolbox functions. Numerical and, respectively, computational aspects are added,
and the corresponding SPECFUNPHYS functions are explained in detail, and some
examples or applications are added.
Content Overview
Chapter 1 covers gamma functions and beta functions and related functions in the
complex domain. Error functions and Fresnel integrals are the topic of Chap. 2,
as well as spectral line profiles such as the Voigt profile and the line broadening
function.
Legendre functions and related functions play an important role in quantum
mechanics, electrodynamics, and so forth and will be discussed in Chap. 3.
Bessel studied the astronomical three-body problem—still a challenge—
and established the Bessel functions in the context of planetary perturbations.
1 MATLAB is a registered trademark of MathWorks, Inc.
v
Special functions arise in many applications of physics, mathematics, chemistry,
and engineering. When writing such a book, one is faced with numerous decisions,
such as: Which special functions and topics should be included? and What should
be assumed about the readers’ prior knowledge? This book is not elementary. The
reader should have a background in mathematics, physics, and programming with
MATLAB. 1
This book deals with computational methods for evaluating special functions
in the real and complex domains. MATLAB was used as programming language.
MATLAB is established at many universities, research institutes, and in industry. The
book comes with an additional toolbox called SPECFUNPHYS toolbox, extending
MATLAB’s capabilities with respect to special functions. The book covers more than
170 special functions mostly in the complex domain, which are either not covered
by standard MATLAB or in standard MATLAB restricted to the real domain.
The presentation of the special functions is organized in 23 chapters, each related
to a family of special functions together with examples or applications. Each chapter
starts with a brief introduction and an overview of the related SPECFUNPHYS
toolbox functions. Numerical and, respectively, computational aspects are added,
and the corresponding SPECFUNPHYS functions are explained in detail, and some
examples or applications are added.
Content Overview
Chapter 1 covers gamma functions and beta functions and related functions in the
complex domain. Error functions and Fresnel integrals are the topic of Chap. 2,
as well as spectral line profiles such as the Voigt profile and the line broadening
function.
Legendre functions and related functions play an important role in quantum
mechanics, electrodynamics, and so forth and will be discussed in Chap. 3.
Bessel studied the astronomical three-body problem—still a challenge—
and established the Bessel functions in the context of planetary perturbations.
1 MATLAB is a registered trademark of MathWorks, Inc.
v