Here is an arbitrary point in the interval . The integration path begins at , encircles once in the positive sense, followed by once in the positive sense, and so on, returning finally to . The integration path is called a Pochhammer double-loop contour (compare Figure 5.12.3). The branches of the many-valued functions are continuous on the path, and assume their principal values at the beginning.
The normalization constant is given by
and denotes the Wronskian (§1.13(i)). The right-hand side may be evaluated at any convenient value, or limiting value, of in since it is independent of .
Heun polynomials , , satisfy
and the integration paths , are Pochhammer double-loop contours encircling distinct pairs of singularities , , .