FunctionAdvisor/singularities
return the poles and essential singularities of a given mathematical function
Calling Sequence
Parameters
Description
Examples
References
FunctionAdvisor(singularities, math_function)
singularities
-
literal name; 'singularities'
math_function
Maple name of mathematical function
The FunctionAdvisor(singularities, math_function) command returns the isolated poles and essential singularities of the function, if any, or the string "No isolated singularities". If the requested information is not available, it returns NULL.
A singularity of at is isolated when is discontinuous at but it is analytic in the neighborhood of . To compute the branch points of a mathematical function, that is, the non-isolated singularities related to the multivaluedness of the function, use the FunctionAdvisor(branch_point, math_function) command.
An isolated singularity can be removable, essential, or a pole. In the call FunctionAdvisor(singularities, math_func) only poles and essential singularities are returned.
An isolated singularity of at is removable when there exists a function such that for and is analytic at . The singularity is a pole when and both are analytic at and . The singularity is essential when it is neither removable nor a pole.
The following are examples of these types of isolated singularities
f1(z) = piecewise(z <> 2, sin(z), z = 2, 0);
f2(z) = 1/(z-3);
f3(z) = exp(1/z);
where has a removable singularity at , has a pole , and has an essential singularity at .
The value of the function at its singularities can typically be checked by direct evaluation or using eval.
Brown, J.W. and Churchill, R.V. Complex Variables and Applications. 6th Ed. McGraw-Hill Science/Engineering/Math, 1995.
See Also
DEtools[singularities]
eval
FunctionAdvisor
FunctionAdvisor/branch_cuts
FunctionAdvisor/branch_points
FunctionAdvisor/topics
singular
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