4th degree algebraic hermite–padé approximation to the exponential function

Abstract

4th Degree algebraic Hermite–Padé approximation to the exponential function with coefficient polynomials of degree at most m is considered. Explicit formulas and differential equations 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.

^*The work is supported by The National Natural Science Foundation of China (Nos 69973010 and 10271022) and The Guangdong Natural Science Foundation of Guangdong Province, China (No. 021755).

Keywords:

• Padé-type approximant
• Cubic Hermite–Padé approximation
• Asymptotic formula
• Differential equation

Notes

^*The work is supported by The National Natural Science Foundation of China (Nos 69973010 and 10271022) and The Guangdong Natural Science Foundation of Guangdong Province, China (No. 021755).