Special Functions for Applied Scientists

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.

Arakaparampil Mathai Mathai was born in Arakulam in the Idukki district of Kerala, India. He is the eldest son of Aley and Arakaparampil Mathai. He completed his High School education in 1953 with record marks in St. Thomas High School, Palai. He then entered St. Thomas College in Palai, obtained his B.Sc. degree in Mathematics in 1957 and went to the University of Kerala, Trivandrum, where he completed his M.Sc. degree in Statistics in 1959 with first class, first rank and a golden medal. He joined St. Thomas College as a lecturer from 1959 to 1961. In 1961, he was awarded a Canadian Commonwealth Scholarship and went to the University of Toronto were he completed an M.A. and a Ph.D. in Mathematics and Mathematical Statistics in only three years, the minimum required time. He then joined McGill University in Montreal - one of the most prestigious universities in Canada - where he was Assistant Professor of Mathematics and Statistics, 1964-1968, Associate Professor, 1968-1978, and Full Professor, 1979-2000. Since 2000, he is Emeritus Professor in Mathematics and Statistics at McGill University, Montreal, Canada. He served and is currently serving on editorial boards of a number of journals and he has supervised over 30 Master's students and 5 Ph.D. students. Currently he is the Director of the Centre for Mathematical Sciences, Trivandrum and Pala Campuses, Kerala, India which he is developing into an national, regional, and international centre of research in the mathematical sciences. The holding of five six-week SERC Schools in 1995, 2000, 2005, 2006, and 2007 are a testament of highest achievements in teaching and research in the mathematical sciences for the Centre.

From the reviews:"Special functions refer to functions, of one or several real or complex variables, that play key roles in ... one area of mathematics, particularly number theory, combinatorics, complex analysis, differential equations, Lie group representations, probability, statistics, and mathematical physics. ... Summing Up: Recommended. Comprehensive academic, technical program, and professional collections, all levels." (D. V. Feldman, Choice, Vol. 46 (5), January, 2009)"This book differs significant from other text books on special functions, because every chapter deals with the topic on one of the courses of the SSF. ... Many examples illustrate the use of theorems and formulas. At the end of each section exercises are given. ... An interesting book for all scientists interested in applications of special functions in physical sciences. It contains a speedy access to many special functions used in applications and also a lot of applications." (H.-J. Glaeske, Zentralblatt MATH, Vol. 1151, 2009)"This book is based on selected lectures given by several speakers at the Centre for Mathematical Sciences ... from 1995 to 2007. ... In the present book these lectures are written up in a style for self-study by scientists, engineers and mathematicians interested in applications ... . Who can profit from this book? Physicists, engineers, other scientists, applied mathematicians, economists, looking for a well-readable introduction ... . this book is surely recommended to open-minded researchers in any scientific and technical area ... ." (Francesco Mainardi, Journal of Approximation Theory, February, 2010)