Extension of the Heaviside Expansion Theorem

Abstract

Heaviside's expansion, x_k=E₁ M_1k(p₀)/M(p₀)εp₀^t-E₁ Σm=n m=1 M_1k(λ_m)ελ_m^t/(p₀-λ_m)M'(λ_m) is valid except in th case M(p₀)=0, p0=λ_m, or M'(λ_m)=0 which makes the value of the expression indeterminate.
In this paper, the writer extended it to expansions which involve such cases.