exceptional values
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1: 28.7 Analytic Continuation of Eigenvalues
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►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).
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2: 28.11 Expansions in Series of Mathieu Functions
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►See Meixner and Schäfke (1954, §2.28), and for expansions in the case of the exceptional values of see Meixner et al. (1980, p. 33).
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3: 5.12 Beta Function
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►In this section all fractional powers have their principal values, except where noted otherwise.
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4: 33.19 Power-Series Expansions in
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►The expansions (33.19.1) and (33.19.3) converge for all finite values of , except
in the case of (33.19.3).
5: 10.72 Mathematical Applications
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►In (10.72.1) assume and depend continuously on a real parameter , has a simple zero and a double pole , except for a critical value
, where .
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6: 8.2 Definitions and Basic Properties
7: 14.21 Definitions and Basic Properties
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and exist for all values of , , and , except possibly and , which are branch points (or poles) of the functions, in general.
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8: 1.4 Calculus of One Variable
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►For the functions discussed in the following DLMF chapters these two integration measures are adequate, as these special functions are analytic functions of their variables, and thus , and well defined for all values of these variables; possible exceptions being at boundary points.
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9: 3.8 Nonlinear Equations
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►The method converges locally and quadratically, except when the wanted quadratic factor is a multiple factor of .
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