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Original Articles

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

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Pages 35-48 | Received 27 Jan 2003, Published online: 08 Jun 2010
 

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).

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).

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