Non Periodic Trigonometric Approximation

The suitable basis functions for approximating periodic function are periodic, trigonometric functions. When the function is not periodic, a viable alternative is to consider polynomials as basis functions. In this paper we will point out the inadequacy of polynomial approximation and suggest a new set of basis functions. The new set does not suffer from the drawbacks of polynomial approximation and by using them one can approximate analytic functions with spectral accuracy.