Basic Ideas of Special Functions and Statistical Distributions -- Mittag-Leffler Functions and Fractional Calculus -- An Introduction to q-Series -- Ramanujan's Theories of Theta and Elliptic Functions -- Lie Group and Special Functions -- Applications to Stochastic Process and Time Series -- Applications to Density Estimation -- Applications to Order Statistics -- Applications to Astrophysics Problems -- An Introduction to Wavelet Analysis -- Jacobians of Matrix Transformations -- Special Functions of Matrix Argument.

Special Functions for Applied Scientists provides the required mathematical tools for researchers active in the physical sciences. The book presents a full suit of elementary functions for scholars at the PhD level and covers a wide-array of topics and begins by introducing elementary classical special functions. From there, differential equations and some applications into statistical distribution theory are examined. The fractional calculus chapter covers fractional integrals and fractional derivatives as well as their applications to reaction-diffusion problems in physics, input-output analysis, Mittag-Leffler stochastic processes and related topics. The authors then cover q-hypergeometric functions, Ramanujan's work and Lie groups. The latter half of this volume presents applications into stochastic processes, random variables, Mittag-Leffler processes, density estimation, order statistics, and problems in astrophysics. Professor Dr. A.M. Mathai is Emeritus Professor of Mathematics and Statistics, McGill University, Canada. Professor Dr. Hans J. Haubold is an astrophysicist and chief scientist at the Office of Outer Space Affairs of the United Nations.