# exceptional values

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##### 1: 28.7 Analytic Continuation of Eigenvalues
The branch points are called the exceptional values, and the other points normal values. The normal values are simple roots of the corresponding equations (28.2.21) and (28.2.22). …
##### 2: 28.11 Expansions in Series of Mathieu Functions
See Meixner and Schäfke (1954, §2.28), and for expansions in the case of the exceptional values of $q$ see Meixner et al. (1980, p. 33). …
##### 3: 5.12 Beta Function
In this section all fractional powers have their principal values, except where noted otherwise. …
##### 4: 33.19 Power-Series Expansions in $r$
The expansions (33.19.1) and (33.19.3) converge for all finite values of $r$, except $r=0$ in the case of (33.19.3).
##### 5: 10.72 Mathematical Applications
In (10.72.1) assume $f(z)=f(z,\alpha)$ and $g(z)=g(z,\alpha)$ depend continuously on a real parameter $\alpha$, $f(z,\alpha)$ has a simple zero $z=z_{0}(\alpha)$ and a double pole $z=0$, except for a critical value $\alpha=a$, where $z_{0}(a)=0$. …
##### 6: 8.2 Definitions and Basic Properties
Except where indicated otherwise in the DLMF these principal values are assumed. …
##### 7: 14.21 Definitions and Basic Properties
$P^{\pm\mu}_{\nu}\left(z\right)$ and $\boldsymbol{Q}^{\mu}_{\nu}\left(z\right)$ exist for all values of $\nu$, $\mu$, and $z$, except possibly $z=\pm 1$ and $\infty$, which are branch points (or poles) of the functions, in general. …
##### 8: 3.8 Nonlinear Equations
The method converges locally and quadratically, except when the wanted quadratic factor is a multiple factor of $q(z)$. …
##### 9: 1.9 Calculus of a Complex Variable
It is single-valued on $\mathbb{C}\setminus\{0\}$, except on the interval $(-\infty,0)$ where it is discontinuous and two-valued. …
##### 10: 3.6 Linear Difference Equations
or for systems of $k$ first-order inhomogeneous equations, boundary-value methods are the rule rather than the exception. …