Sons, Linda R.
M.S. (Master of Science)
Department of Mathematics
Most books on advanced calculus contain sane discussion of the gamma function. Usually the development of the properties of this function is obtained by relating two distinct definitions of the function and deriving some properties using one definition and others using a second definition. This paper contains four particular definitions of the functions. After showing the equivalence of the definitions, the following properties are developed for each definition in turn; these are r(x + 1) = x r(x), a form of the logarithmic derivative, the trigonometric relation, the duplication formula, and log convexity. The gamma function can also be considered as a unique solution of a certain difference equation satisfying certain properties. This paper considers solving variations of the equation f(x + 1) = x f(x) with combinations of gamma functions as solutions. Several theorems are given showing solutions of h(x + 1) = R(x) h(x) and x(x + 1) - x(x) =1/x which involve gamma function.
Kronebusch, John Jacob, "Investigations of the gamma function" (1967). Graduate Research Theses & Dissertations. 3664.
Northern Illinois University
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