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1: 31.12 Confluent Forms of Heun’s Equation
This has one singularity, an irregular singularity of rank 3 at z = . 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). …
2: 14.29 Generalizations
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
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
For properties of these solutions see Arscott (1964b, §9.7), Erdélyi et al. (1955, §15.5.1), Shail (1980), and Sleeman (1966b). … Lamé–Wangerin functions are solutions of (29.2.1) with the property that ( sn ( z , k ) ) 1 / 2 w ( z ) is bounded on the line segment from i K to 2 K + i K . …
5: 28.5 Second Solutions fe n , ge n
S 2 m + 2 ( - q ) = S 2 m + 2 ( q ) .
6: 10.25 Definitions
This solution has properties analogous to those of J ν ( z ) , defined in §10.2(ii). … The defining property of the second standard solution K ν ( z ) of (10.25.1) is …
7: 16.23 Mathematical Applications
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. …
8: 9.2 Differential Equation
9.2.1 d 2 w d z 2 = z w .
9.2.16 d W d z + W 2 = z ,
9: 31.6 Path-Multiplicative Solutions
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 s 1 and s 2 once in the positive sense, but not the remaining finite singularity, then the solution is multiplied by a constant factor e 2 ν π i . …
10: 14.21 Definitions and Basic Properties