| Summary: | A research report submitted to the Faculty of Science,
University of the Witwatersrand, in fulfilment of the
requirements for the degree of Master of Science.
Johannesburg, 2013 === Equations involving the gamma and hypergeometric functions are of great interest to
mathematicians and scientists, and newly proven identities for these functions assist
in finding solutions to differential and integral equations.
In this work we trace a brief history of the development of the gamma and
hypergeometric functions, illustrate the close relationship between them and present a
range of their most useful properties and identities, from the earliest ones to those
developed in more recent years. Our literature review will show that while continued
research into hypergeometric identities has generated many new results, some of
these can be shown to be variations of known identities. Hence, we will also discuss
computer based methods that have been developed for creating and analysing such
identities, in order to check for originality and for numerical validity.
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