AbstractsMathematics

"It is the purpose of this study to survey the properties of the Tschebyscheff polynomials with particular reference to how they are employed as approximants and interpolants. The survey is extended to include the process known as "Tschebyscheff Approximation" or "Tschebyscheff Fitting" of a function by functions other than polynomials. One such fitting technique which will be of particular interest in this study is that of fitting f(x) by the function ab[superscript x] + c where a, b, c are real and b [symbol for does not equal] 1. In addition to a survey of the properties of the Tschebyscheff polynomials and of Tschebyscheff fitting techniques, computer-programmed illustrations will be presented to demonstrate the practicability of fitting functions by Tschebyscheff polynomials and other special functions. In addition to the computation of the parameters, a computer-programmed plotting of the function and its approximants is also displayed" – Introduction, p. 1.