Publication Date

1967

Document Type

Dissertation/Thesis

First Advisor

Sons, Linda R.

Degree Name

M.S. (Master of Science)

Legacy 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.

Comments

Includes bibliographical references (leaf 47)

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

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