Date of Award
Master of Arts
As early as the seventeenth century the English mathematician, john Wallis (1616-1703), used the term "hypergeometric" to describe a series which he was studying. This series, ∑(a)(a+b)(a+2b)…(a+n-1b), is quite different from the usual geometric series, hence the term, "hyper" (=above) plus "geometric," was used to signify that the series was of greater complexity than the geometric series. Wallis did not consider his series a power series or a function of x.
In 1769 this series received a remarkable development at the hands of Loonhard Euler who, following the example of Wallis, applied the word "hypergeometric" to it. He observed that the series is dependent upon the integration of a linear partial differtial equation of the second order. In his work the series is treated from three distinct standpoint: (i) as a power series, (ii) as an integral of a certain linear equation of the second order, (iii) and as a definite integral.2
Smith, William R., "Gauss' hypergeometric equation" (1939). Master's Theses. 1151.