Accelerating the convergence of power series of certain entire functions (Q1819528)

Due to cancellation, the numerical evaluation of an entire function by its Taylor series expansion may become a difficult task whenever terms of large modulus are required to evaluate a small result. In this paper, we propose methods to evaluate entire functions of order 1 and finite positive type. It is shown that this problem may be reduced to the approximation of the exponential function by polynomials. Thus, polynomial interpolation of exp(y) gives an effective tool to accelerate the convergence of the Taylor series. After having done this successfully we consider an example and find that incidentally the problem of large alternating terms has been mitigated.