Partial Fractions

Under what conditions can the function \displaystyle \frac{1}{x^{2}-4x+3} be expanded (i) as a power series in x; (ii) as a power series in \displaystyle \frac{1}{x}?  Find the coefficients of x^{n} and \displaystyle \frac{1}{x^{n-1}} in the two expansions.

Source: Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Miscellaneous Examples, Question 13, p. 221)

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

Leave a Reply