用于积分方程解的函数值Padé逼近的Pfaffin公式

1　Introduction　Letf(x ,λ)beagivenpowerserieswithfunction valuedcoefficients,f(x ,λ) =c0 (x) c1(x)λ c2 (x)λ2 … 　　cn(x)λn … (1)wherecj(x)isarealorcomplexfunctionwithre specttox∈ (a ,b) .Suppoethatf(x ,λ)isanalyticasafunctionofλattheoriginλ =0 .　Chisholm[1] pointedoutPad啨ａｐｐｒｏｘｉｍａｎｔｍｅｔｈｏｄｃａｎｂｅｕｓｅｄｆｏｒｏｂｔａｉｎｉｎｇｔｈｅｓｏｌｕｔｉｏｎｏｆａｗｋｗａｒｄｉｎ tegralequations,andespeciallythosewhichpossessageneratingfunctionoftheform (1) ,sinceth…     

A Pfaffian Formula of the Generalized Inverse Function-Valued Pade Approximant Used in Solving Integral Equations

The generalized inverse function-valued Pade approximant was defined to solve the integral equations. However, it is difficult to compute the approximants by some high-order determinant formulas. In this paper, to simplify computation of the function-valued Pade approximants, an efficient Pfaffian formula for the determinants was extended from the matrix form to the function-valued form. As an important application, a Pfaffian formula of [4/4] type Pade approximant was established.