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.
