properties of solutions
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1: 31.12 Confluent Forms of Heun’s Equation
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►This has one singularity, an irregular singularity of rank at .
►For properties of the solutions of (31.12.1)–(31.12.4), including connection formulas, see Bühring (1994), Ronveaux (1995, Parts B,C,D,E), Wolf (1998), Lay and Slavyanov (1998), and Slavyanov and Lay (2000).
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2: 14.29 Generalizations
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►For inhomogeneous versions of the associated Legendre equation, and properties of their solutions, see Babister (1967, pp. 252–264).
3: 29.11 Lamé Wave Equation
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►For properties of the solutions of (29.11.1) see Arscott (1956, 1959), Arscott (1964b, Chapter X), Erdélyi et al. (1955, §16.14), Fedoryuk (1989), and Müller (1966a, b, c).
4: 29.17 Other Solutions
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►For properties of these solutions see Arscott (1964b, §9.7), Erdélyi et al. (1955, §15.5.1), Shail (1980), and Sleeman (1966b).
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►Lamé–Wangerin functions are solutions of (29.2.1) with the property that is bounded on the line segment from to .
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5: 28.5 Second Solutions ,
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6: 10.25 Definitions
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►This solution has properties analogous to those of , defined in §10.2(ii).
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►The defining property of the second standard solution
of (10.25.1) is
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7: 16.23 Mathematical Applications
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►These equations are frequently solvable in terms of generalized hypergeometric functions, and the monodromy of generalized hypergeometric functions plays an important role in describing properties of the solutions.
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8: 9.2 Differential Equation
9: 31.6 Path-Multiplicative Solutions
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►This denotes a set of solutions of (31.2.1) with the property that if we pass around a simple closed contour in the -plane that encircles and once in the positive sense, but not the remaining finite singularity, then the solution is multiplied by a constant factor .
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10: 14.21 Definitions and Basic Properties
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