Perturbed Chebyshev rational approximation

In this work, we give a perturbed Chebyshev rational approximation for a function f (x) which has a Chebyshev expansion. This approximation contains a perturbation parameter ~ which is calculated so that the perturbed Chebyshev rational approximation agrees with the Chebyshev expansion to a certain number of terms. Also, we introduce a perturbed Chebyshev rational approximation for the definite integral of a function f (x) having Chebyshev expansion and show that this method can be used iteratively to approximate the multiple integral of the considered function. The method has been applied to approximate some functions and their definite integrals.

Keywords:

• Chebyshev Expansion
• Chebyshev Rational Approximation