一类特殊函数的[n/n]Padé逼近

本文对［ｎ／ｎ］Ｐａｄé逼近进行探讨，证明了Ｐｎ（ｘ）／Ｑｎ（ｘ）是函数ｆ（ｘ）在ｘ＝０处的［ｎ／ｎ］Ｐａｄé逼近，而Ｑｎ（ｘ）＝Ｐｎ（－ｘ）的充要条件是ｆ（ｘ）ｆ（－ｘ）＝１，从而使这一类函数的［ｎ／ｎ］Ｐａｄé逼近计算量减少一半．

The Padé Approximants for a Class of Special Functions

In this paper, we discussed further the Padé approximants, and proved P n(x)/Q n(x) is the function f(x) 's Padé approximant at x=0 (where P n(x), Q n(x) are all polynomial of degree n ) and Q n(x)=P n(-x) if and only if f(x)·f(-x)=1 , therefore the calculation quantity of the kinds of functions's Padé approximants decrease to half.