The Hardy-Ramanujan-Rademacher expansion for \(c\phi{}_{m,m'}(n)\) using Ford circles (Q1189883)

\textit{Padmavathamma} [J. Ramanujan Math. Soc. 2, 1-16 (1987; Zbl 0669.10026)] obtained a convergent asymptotic series for the function \(c\phi_{m,m'}(n)\) which counts the number of generalized Frobenius partitions of \(n\) with \(m\) colors and \(m'\) repetitions, using the Hardy- Ramanujan circle method as was done earlier in the 1985 Ph. D. Thesis of L. W. Kolitsch for the special cases \(c\phi_{1,m'}(n)\) and \(c\phi_{m,1}(n)\). This paper gives another derivation based on Rademacher's method in treating the ordinary partition function \(p(n)\) employing Ford circles as the path of integration.