Cubic Hermite–Padé approximation to the exponential function

摘要

Cubic Hermite–Padé approximation to the exponential function with coefficient polynomials of degree at most m is considered. Explicit formulas are obtained for the coefficient polynomials. An exact asymptotic expression is obtained for the error function and it is also shown that these generalized Padé-type approximations can be used to asymptotically minimize the expressions on the unit disk.