The odd-order radial limit of Ramanujan's third-order mock theta function

We prove that for every odd integer k ≥ 3 and every primitive kth root of unity ζₖ, limₑ→₁⁻ f (rζₖ) = (4/3) ·Tₖ, where Tₖ is a finite cyclotomic sum in ℤζₖ. This is the odd-order companion to the Folsom–Ono–Rhoades even-order radial limit formula. The factor 4/3 arises from the k-periodicity of the q-Pochhammer symbol on the unit circle: each complete cycle contributes a factor of 2, squaring in the denominator yields 4, and the resulting geometric series collapses to 4/3.