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11: 16.2 Definition and Analytic Properties
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►Elsewhere the generalized hypergeometric function is a multivalued function that is analytic except for possible branch points at , and .
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►When and is fixed and not a branch point, any branch of is an entire function of each of the parameters .
12: 4.13 Lambert -Function
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is a single-valued analytic function on , real-valued when , and has a square root branch point at .
…The other branches
are single-valued analytic functions on , have a logarithmic branch point at , and, in the case , have a square root branch point at respectively.
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13: 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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14: 10.61 Definitions and Basic Properties
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►In general, Kelvin functions have a branch point at and functions with arguments are complex.
The branch point is absent, however, in the case of and when is an integer.
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15: 32.2 Differential Equations
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►An equation is said to have the Painlevé property if all its solutions are free from movable branch points; the solutions may have movable poles or movable isolated essential singularities (§1.10(iii)), however.
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16: 10.25 Definitions
17: 4.23 Inverse Trigonometric Functions
18: 4.2 Definitions
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►This is a multivalued function of with branch point at .
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►In all other cases, is a multivalued function with branch point at .
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19: Bibliography H
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The eigenvalues of Mathieu’s equation and their branch points.
Stud. Appl. Math. 64 (2), pp. 113–141.
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