# large κ

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## 11—20 of 152 matching pages

##### 11: Karl Dilcher
Over the years he authored or coauthored numerous papers on Bernoulli numbers and related topics, and he maintains a large on-line bibliography on the subject. …
##### 12: 10.70 Zeros
###### §10.70 Zeros
Asymptotic approximations for large zeros are as follows. …If $m$ is a large positive integer, then …
##### 13: 35.10 Methods of Computation
For large $\|\mathbf{T}\|$ the asymptotic approximations referred to in §35.7(iv) are available. … These algorithms are extremely efficient, converge rapidly even for large values of $m$, and have complexity linear in $m$.
##### 16: 15.12 Asymptotic Approximations
###### §15.12(ii) Large$c$
For large $b$ and $c$ with $c>b+1$ see López and Pagola (2011).
###### §15.12(iii) Other Large Parameters
For other extensions, see Wagner (1986), Temme (2003) and Temme (2015, Chapters 12 and 28).
##### 20: 11.13 Methods of Computation
Although the power-series expansions (11.2.1) and (11.2.2), and the Bessel-function expansions of §11.4(iv) converge for all finite values of $z$, they are cumbersome to use when $|z|$ is large owing to slowness of convergence and cancellation. For large $|z|$ and/or $|\nu|$ the asymptotic expansions given in §11.6 should be used instead. … Then from the limiting forms for small argument (§§11.2(i), 10.7(i), 10.30(i)), limiting forms for large argument (§§11.6(i), 10.7(ii), 10.30(ii)), and the connection formulas (11.2.5) and (11.2.6), it is seen that $\mathbf{H}_{\nu}\left(x\right)$ and $\mathbf{L}_{\nu}\left(x\right)$ can be computed in a stable manner by integrating forwards, that is, from the origin toward infinity. The solution $\mathbf{K}_{\nu}\left(x\right)$ needs to be integrated backwards for small $x$, and either forwards or backwards for large $x$ depending whether or not $\nu$ exceeds $\tfrac{1}{2}$. …