A note on the relative merits of Padé and Maehly’s diagonal convergents in computing $e^{x}$

Abstract:

Methods for calculating functions to a high degree of accuracy have assumed increased importance following the advent of the computers. It has been found that rational approximations require fewer operations on a computer than the older polynomial approximations. Among the known methods those due to Padé [1] and Maehly [2] are perhaps the most important. In this paper we have analyzed these methods as applied to the exponential function. It is observed that Maehly’s method is superior to the Padé method in the sense of yielding better accuracy over a given range on the real axis for a given order of approximation. Maehly’s formulas for computing ${e^x}$ correct to eight decimal places have been worked out.