Chapter 1 introduces elementary classical special functions.
Gamma, beta, psi, zeta functions, hypergeometric functions and the
associated special functions, generalizations to Meijer's G and
Fox's H-functions are examined here. Discussion is confined to
basic properties and selected applications. Introduction to
statistical distribution theory is provided. Some recent extensions
of Dirichlet integrals and Dirichlet densities are discussed. A
glimpse into multivariable special functions such as Appell's
functions and Lauricella functions is part of Chapter 1. Special
functions as solutions of differential equations are examined.
Chapter 2 is devoted to fractional calculus. Fractional integrals
and fractional derivatives are discussed. Their applications to
reaction-diffusion problems in physics, input-output analysis, and
Mittag-Leffler stochastic processes are developed. Chapter 3 deals
with q-hyper-geometric or basic hypergeometric functions. Chapter 4
covers basic hypergeometric functions and Ramanujan's work on
elliptic and theta functions. Chapter 5 examines the topic of
special functions and Lie groups. Chapters 6 to 9 are devoted to
applications of special functions. Applications to stochastic
processes, geometric infinite divisibility of random variables,
Mittag-Leffler processes, alpha-Laplace processes, density
estimation, order statistics and astrophysics problems, are dealt
with in Chapters 6 to 9. Chapter 10 is devoted to wavelet analysis.
An introduction to wavelet analysis is given. Chapter 11 deals with
the Jacobians of matrix transformations. Various types of matrix
transformations and the associated Jacobians are provided. Chapter
12 is devoted to the discussion of functions of matrix argument in
the real case. Functions of matrix argument and the pathway models
along with their applications are discussed.
General
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