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path-multiplicative solutions

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1: 31.6 Path-Multiplicative Solutions
§31.6 Path-Multiplicative Solutions
A further extension of the notation (31.4.1) and (31.4.3) is given by …These solutions are called path-multiplicative. …
2: 31.9 Orthogonality
and the integration paths 1 , 2 are Pochhammer double-loop contours encircling distinct pairs of singularities { 0 , 1 } , { 0 , a } , { 1 , a } . … For bi-orthogonal relations for path-multiplicative solutions see Schmidt (1979, §2.2). …
3: 31.11 Expansions in Series of Hypergeometric Functions
§31.11(v) Doubly-Infinite Series
Schmidt (1979) gives expansions of path-multiplicative solutions31.6) in terms of doubly-infinite series of hypergeometric functions. …
4: 31.10 Integral Equations and Representations
For suitable choices of the branches of the P -symbols in (31.10.9) and the contour C , we can obtain both integral equations satisfied by Heun functions, as well as the integral representations of a distinct solution of Heun’s equation in terms of a Heun function (polynomial, path-multiplicative solution). …