Write Θ~E for the stable discrete series character associated with an irreducible finite-dimensional representation E of a connected real reductive group G. Let M be the centralizer of the split component of a maximal torus T, and denote by φ_M(γ, Θ~E) Arthur's extension of |D~G_M(γ) |~(1/2)Θ~E(γ) to T(R). In this paper we give a simple explicit expression for Φ_M(γ, Θ~E) when γ is elliptic in G. We do not assume γ is regular.
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