properties of solutions

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1: 31.12 Confluent Forms of Heun’s Equation
This has one singularity, an irregular singularity of rank $3$ at $z=\infty$. 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 $(\operatorname{sn}\left(z,k\right))^{1/2}w(z)$ is bounded on the line segment from $\mathrm{i}{K^{\prime}}$ to $2K+\mathrm{i}{K^{\prime}}$. …
5: 28.5 Second Solutions $\operatorname{fe}_{n}$, $\operatorname{ge}_{n}$
$S_{2m+2}(-q)=S_{2m+2}(q).$
6: 10.25 Definitions
This solution has properties analogous to those of $J_{\nu}\left(z\right)$, defined in §10.2(ii). … The defining property of the second standard solution $K_{\nu}\left(z\right)$ 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 $\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}=zw.$
9.2.16 $\frac{\mathrm{d}W}{\mathrm{d}z}+W^{2}=z,$
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 ${\mathrm{e}}^{2\nu\pi i}$. …