Physical Sciences and Mathematics Commons^™

Gauss' Hypergeometric Equation, William R. Smith

Master's Theses

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 Kolbe Synthesis With Alkyl Ortho-Xenols, Sidney Harris

Master's Theses

The phenol series of compounds has shown marked therapeutic activity. Generally there are two types phenols used as germicides and fungicides - (a) the very soluble type such as the resorcinols and ( b) the less soluble type such as the phenyl phenols and salicylic acid and its derivatives.

Condensation Of Olefins With P-Mercapto-Diphenyl, Raymond Michael Abrams

Master's Theses

Markownikow's rule states that in the addition to unsaturated ,negative groups add to the carbon atom having the least number of Hydrogen atoms. It has been observed that mercaptans and hydrogen sulfide add to olefine contrary to Markownikow's rule in the presence of sodium alcoholates or sulfuric acid.