(f,g)-反演的函数方程的通解

General Solution of(f,g)-Inversion

马欣荣建立了迄今为止广泛的一对反演公式(f,g)-反演,它完全取决于所给的一对函数f,g是否满足函数方程g(a,b)f(x,c)-g(a,c)f(x,b)+g(b,c)f(x,a)=0。本文就f,g为多项式和无穷级数时给出了上述方程的通解。

The main purpose of the present paper is to find the explicit expressions of fand g such that g （ a, b ）f（x, c ） -g （ a, c ）f（ x, b ） ＋g （ b, c ）f（x, a ） =0. with the assumption that f and g are polynomials or infinite series. As we will see later, such a pair of functions f and g always leads us to the （f,g）- inversion due to Ma[l] which is of value to the basic hvoerzeometric series.