The purpose of this thesis is to provide a beginning graduate student in mathematics with the general theory underlying competition between rational, intelligent opponents. This competition can be described as a game of opposing strategies; hence, the name game theory.
This paper shall be mostly concerned with the development and the properties of three quadratic polynomials. The primary interest will by with n-ary quadratic polynomials, called forms.
This study involves the ultraspherical polynomials, the Legendre polynomials, the Tchebichef polynomials of the first kind, and the Tchebichef polynomials of the second kind.
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