Abstract
In this paper a unified recursive algorithm is realized to determine the partial fraction expansion coefficients of of the most general form of rational functions without any kind of distinction.
(1) Fundamental recurrence formulae are derived for the expansion of the product of two kinds of multiple poles, and for the Laurent series expansion of numerator polynomials.
(2) Coefficients a (l, i) of the Laurent series expansion of denominator 1/Q(z), and b(l, i) of the numerator polynomial P(z) are given by the iterative use of these recursive formulate.
(3) The product of the coefficients a (l, i) and b(l, i) constitutes the partial fraction expansion coefficients c(l, i) and c0(l) of P(z)/Q(z).
The algorithm is suitable both for machine calculation and for figures.
The application of the algorithm to computer programs is discussed.
The accuracy of the calculated values of coefficients clarifies the effectiveness of the algorithm.
