The theory of generalized hypergeometric functions is fundamental
in the field of mathematical physics, since all the commonly used
functions of analysis (Besse] Functions, Legendre Functions, etc.)
are special cases of the general functions. The unified theory
provides a means for the analysis of the simpler functions and can
be used to solve the more complicated equations in physics. The
generalized Gauss function is also used in mathematical statistics
and the basic analogues of the Gauss functions have applications in
the field of number theory. Dr Slater's treatment leads on from a
discussion of the Gauss functions to the basic hypergeometric
functions, the hypergeometric integrals, bilateral series and Appel
series. This book was planned jointly with the late Professor W. N.
Bailey as an extended revision of his Cambridge Mathematical Tract
(1935) on the subject and Dr Slater has continued it single-handed
since Professor Bailey's death, incorporating in it the results of
many of her own researches.
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