4 research outputs found
Identities for the gamma and hypergeometric functions: an overview from Euler to the present
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, 2013Equations 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
Mathematical Analysis and Applications
Investigations involving the theory and applications of mathematical analytic tools and techniques are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. In this Special Issue, we invite and welcome review, expository and original research articles dealing with the recent advances in mathematical analysis and its multidisciplinary applications
The different tongues of q-calculus
In this review paper we summarize the various dialects of q-calculus: quantum calculus, time scales, and partitions. The close connection between Γq(x) functions on the one hand, and elliptic functions and theta functions on the other hand will be shown. The advantages of the Heine notation will be illustrated by the (q-)Euler reflection formula, q-Appell functions, Carlitz– AlSalam polynomials, and the so-called q-addition. We conclude with some short biographies about famous scientists in q-calculus