Fitting combinations of exponentials to probability distributions

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Valuing equity-linked death benefits in jump diffusion models (2013, background): “For finding a combination of exponential distributions to approximate the distribution of Tx, fTx(t) ≈ ∑ j cjfτj(t), (11.1) two papers by Dufresne (2007a, 2007b) are helpful.”
On the Class of Erlang Mixtures with Risk Theoretic Applications (2007, background): “We remark that the closely related combination of exponentials distribution is dense in the space of positive continuous distributions (Dufresne 2006), a property shared with the class of Erlang mixtures themselves, as was alluded to in the introduction.”
Modeling and Evaluating Insurance Losses Via Mixtures of Erlang Distributions (2010, methodology): “Dufresne (2007) proposes a solution by introducing Jacobian polynomials.”
Valuing equity-linked death benefits and other contingent options: A discounted density approach (2012, background): “Now, combinations of exponential distributions are (weakly) dense in the space of all probability distributions on the positive axis (Dufresne, 2007a,b; Ko and Ng, 2007); see also Section 3 in Shang et al. (2011). Thus, if we can find a formula for the expectation E[eb(S(τ ))], (1.”