Digital Library of Mathematical Functions
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§31.6 Path-Multiplicative Solutions

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

31.6.1 (s1,s2)Hfmν(a,qm;α,β,γ,δ;z),
m=0,1,2,,

with (s1,s2){0,1,a}, but with another set of {qm}. 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 s1 and s2 once in the positive sense, but not the remaining finite singularity, then the solution is multiplied by a constant factor 2νπ. These solutions are called path-multiplicative. See Schmidt (1979).