# path-multiplicative solutions

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## 4 matching pages

##### 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

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►and the integration paths
${\mathcal{L}}_{1}$, ${\mathcal{L}}_{2}$ are Pochhammer double-loop contours encircling distinct pairs of singularities $\{0,1\}$, $\{0,a\}$, $\{1,a\}$.
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►For bi-orthogonal relations for path-multiplicative solutions see Schmidt (1979, §2.2).
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##### 3: 31.11 Expansions in Series of Hypergeometric Functions

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###### §31.11(v) Doubly-Infinite Series

►Schmidt (1979) gives expansions of path-multiplicative solutions (§31.6) in terms of doubly-infinite series of hypergeometric functions. …##### 4: 31.10 Integral Equations and Representations

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►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).
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