removable discontinuity

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21: 8.12 Uniform Asymptotic Expansions for Large Parameter

… ►The right-hand sides of equations (8.12.9), (8.12.10) have removable singularities at $\eta =0$, and the Maclaurin series expansion of $c_k(\eta )$ is given by … ►A different type of uniform expansion with coefficients that do not possess a removable singularity at $z=a$ is given by …

22: 18.40 Methods of Computation

… ►Results similar to these appear in Langhoff et al. (1976) in methods developed for physics applications, and which includes treatments of systems with discontinuities in $\mu (x)$, using what is referred to as the Stieltjes derivative which may be traced back to Stieltjes, as discussed by Deltour (1968, Eq. 12). …

23: 28.12 Definitions and Basic Properties

… ►As a function of $\nu$ with fixed $q$ ($\ne 0$), ${\lambda }_{\nu }\left(q\right)$ is discontinuous at $\nu =\pm 1,\pm 2,\mathrm{\dots }$. …

24: Bibliography D

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Asymptotics of the generalized exponential integral, and error bounds in the uniform asymptotic smoothing of its Stokes discontinuities. Proc. Roy. Soc. London Ser. A 452, pp. 1351–1367.

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External Links:

ISSN 0962-8444, FullText, MathReview (Alexander Tovbis), ZentralBlatt

Referenced by:

§2.11(iii), §8.20(ii).

Encodings:

BibTeX

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25: 4.37 Inverse Hyperbolic Functions

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26: 3.1 Arithmetics and Error Measures

… ►During the calculations common divisors are removed from the rational numbers, and the final results can be converted to decimal representations of arbitrary length. …

27: 11.6 Asymptotic Expansions

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28: 16.5 Integral Representations and Integrals

… ►In (16.5.3) the restriction can be removed when . …

29: 18.1 Notation

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30: 25.11 Hurwitz Zeta Function

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25.11.36Removed because it is just (25.15.1) combined with (25.15.3).

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Symbols:

$L(s,\chi )$: Dirichlet $L$-function and $k$: nonnegative integer

Referenced by:

§25.11(x), Erratum (V1.0.23) for Equation (25.11.36), Erratum (V1.0.23) for Equation (25.11.36)

Permalink:

http://dlmf.nist.gov/25.11.E36

Removal (effective with 1.1.4):

This equation has been removed because it is just (25.15.1) combined with (25.15.3).

Clarification (effective with 1.0.23):

The Dirichlet $L$-function was inserted on the left-hand side. The upper-index of the finite sum which originally was $k$, was replaced with $k-1$ since $\chi (k)=0$.

See also:

Annotations for §25.11(x), §25.11 and Ch.25

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