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Note on Partial Fractions and Determinants

Published online by Cambridge University Press:  20 January 2009

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In looking for a compact way of writing down the partial fraction formula in general, with repeated factors, I noticed how the expansion of a determinant by its top or bottom row suggested a method. The following gives a formula perfectly easy to write down in any given case where the factors of the denominator of the fraction are known. Incidentally it gives, as a determinant, the integral of a rational fraction f(x)/Q(x) where f(x) and Q(x) are polynomials, Q(x) having higher order.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1927

References

page 51 note 1 History, I, p. 339. Jacobi (1841).Google Scholar

page 53 note 1 CfMuir, . Historg IV, p. 178. Schendel appears first to have discussed this type of determinant.Google Scholar