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1: 36.4 Bifurcation Sets
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§36.4(i) Formulas
►Critical Points for Cuspoids
… ►Critical Points for Umbilics
… ►This is the codimension-one surface in space where critical points coalesce, satisfying (36.4.1) and … ►This is the codimension-one surface in space where critical points coalesce, satisfying (36.4.2) and …2: 25.12 Polylogarithms
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►Other notations and names for include (Kölbig et al. (1970)), Spence function (’t Hooft and Veltman (1979)), and (Maximon (2003)).
►In the complex plane has a branch point at .
The principal branch has a cut along the interval and agrees with (25.12.1) when ; see also §4.2(i).
The remainder of the equations in this subsection apply to principal branches.
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3: 28.7 Analytic Continuation of Eigenvalues
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►The only singularities are algebraic branch points, with and finite at these points.
The number of branch points is infinite, but countable, and there are no finite limit points.
…The branch points are called the exceptional values, and the other points normal values.
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►For a visualization of the first branch point of and see Figure 28.7.1.
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4: 3.1 Arithmetics and Error Measures
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►A nonzero normalized binary floating-point machine number
is represented as
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IEEE Standard
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…5: 4.2 Definitions
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►This is a multivalued function of with branch point at .
►The principal value, or principal branch, is defined by
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►Most texts extend the definition of the principal value to include the branch cut
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►In all other cases, is a multivalued function with branch point at .
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►This result is also valid when has its principal value, provided that the branch of satisfies
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6: Mark J. Ablowitz
7: 4.3 Graphics
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►Corresponding points share the same letters, with bars signifying complex conjugates.
…In the labeling of corresponding points
is a real parameter that can lie anywhere in the interval .
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8: 1.10 Functions of a Complex Variable
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►Then is a branch point of .
For example, is a branch point of .
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►(a) By introducing appropriate cuts from the branch points and restricting to be single-valued in the cut plane (or domain).
►(b) By specifying the value of at a point
(not a branch point), and requiring to be continuous on any path that begins at and does not pass through any branch points or other singularities of .
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9: 10.2 Definitions
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►This solution of (10.2.1) is an analytic function of , except for a branch point at when is not an integer.
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►Whether or not is an integer has a branch point at .
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►Each solution has a branch point at for all .
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