A further extension of the notation (31.4.1) and (31.4.3) is given by

with $(s_1,s_2)\in \{0,1,a\}$, but with another set of $\{q_m\}$. This denotes a set of solutions of (31.2.1) with the property that if we pass around a simple closed contour in the $z$-plane that encircles $s_1$ and $s_2$ once in the positive sense, but not the remaining finite singularity, then the solution is multiplied by a constant factor ${\mathrm{e}}^{2\nu \pi \mathrm{i}}$. These solutions are called path-multiplicative. See Schmidt (1979).