I have attempted to 'write this book in such a way that it can be read not only by professional mathematicians, physicists, engineers, and chemists, but also by \yell-trained graduate students in those and closely allied fields. Even the research worker in special functions may notice, however, some results or techniques with which he is not already familiar.

Many of the standard concepts and methods which are useful in the detailed study of special functions are included. The reader will also find here other tools, such as the Sheffer classification of polynomial sets and Sister Celine's technique for obtaining recurrence relations, which deserve to become more widely used.

Those who know me will not be surprised to find a certain emphasis on generating functions and their w,efulness. That functions of hypergeometric character pervade the bulk of the book is but n reflection of their frequent occurrence in the subject itself.

More than fifty special functions appear in this work, some of them treated extensively, others barely mentioned. There are dozens of topics, numerous methods, and hundreds of specinl funrtiolls \vhich could well have been included but which have been omitted. The temptation to approach the subject on the encyclopedic level intended by the late Harry Bateman was great. To me it seems that such an approach \vould have resulted in less, rather than more, usefulness; the work would never have reached the stage of publication.

The short bibliography at the end of the book should give the reader ample material \'lith which to start on a more thorough study of the field.

This book is based upon the lectures on Special Functions which I have been giving at The University of Michigan since 1946. The enthusiastic reception accorded the course here has encouraged me to present the material in a form which may facilitate the teaching of similar courses elsewhere.