#### Publication Date

1967

#### Document Type

Dissertation/Thesis

#### First Advisor

Sons, Linda R.

#### Degree Name

M.S. (Master of Science)

#### Department

Department of Mathematics

#### LCSH

Gamma functions

#### Abstract

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.

#### Recommended Citation

Kronebusch, John Jacob, "Investigations of the gamma function" (1967). *Graduate Research Theses & Dissertations*. 3664.

https://huskiecommons.lib.niu.edu/allgraduate-thesesdissertations/3664

#### Extent

47 pages

#### Language

eng

#### Publisher

Northern Illinois University

#### Rights Statement

In Copyright

#### Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

#### Media Type

Text

## Comments

Includes bibliographical references (leaf 47)