About the Project
NIST

removable singularity

AdvancedHelp

(0.001 seconds)

5 matching pages

1: 1.10 Functions of a Complex Variable
This singularity is removable if a n = 0 for all n < 0 , and in this case the Laurent series becomes the Taylor series. …Lastly, if a n 0 for infinitely many negative n , then z 0 is an isolated essential singularity. … An isolated singularity z 0 is always removable when lim z z 0 f ( z ) exists, for example ( sin z ) / z at z = 0 . …
2: 8.12 Uniform Asymptotic Expansions for Large Parameter
The right-hand sides of equations (8.12.9), (8.12.10) have removable singularities at η = 0 , and the Maclaurin series expansion of c k ( η ) is given by … A different type of uniform expansion with coefficients that do not possess a removable singularity at z = a is given by …
3: 1.4 Calculus of One Variable
A removable singularity of f ( x ) at x = c occurs when f ( c + ) = f ( c - ) but f ( c ) is undefined. … …
4: 21.7 Riemann Surfaces
Removing the singularities of this curve gives rise to a two-dimensional connected manifold with a complex-analytic structure, that is, a Riemann surface. All compact Riemann surfaces can be obtained this way.
5: 25.2 Definition and Expansions
It is a meromorphic function whose only singularity in is a simple pole at s = 1 , with residue 1. …
25.2.4 ζ ( s ) = 1 s - 1 + n = 0 ( - 1 ) n n ! γ n ( s - 1 ) n ,