A formal power-series can be thought as a polynomial with infinitely many terms. From the Cauchy-product, we can gain the coefficients of product of two power-series (product-coefficients) by the coefficients of each two series directly. But for division of two such power-series, we must use the division-algorithm to get the coefficients of the quotient power-series (division-coefficients). This can be done iteratively, i.e. you can get each division-coefficient after getting all of the previous division-coefficients. In this paper, we have found these division coefficients directly by a determinant of coefficients of each two series. For an application, some well-formed determinants can be gained by this determinant. Especially, the determinant of some block-tridiagonal matrices can be determined by this manner which it can’t be gained with the algorithms by others.
کلید واژگان :Power-series, Cauchy-product, Division algorithm, block-tridiagonal matrices
ارزش ریالی : 300000 ریال
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