About the Project
NIST

large κ

AdvancedHelp

(0.001 seconds)

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 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 .
14: 13.19 Asymptotic Expansions for Large Argument
§13.19 Asymptotic Expansions for Large Argument
15: 10.69 Uniform Asymptotic Expansions for Large Order
§10.69 Uniform Asymptotic Expansions for Large Order
16: 15.12 Asymptotic Approximations
§15.12(i) Large Variable
§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).
17: 33.21 Asymptotic Approximations for Large | r |
§33.21 Asymptotic Approximations for Large | r |
§33.21(i) Limiting Forms
§33.21(ii) Asymptotic Expansions
18: 8.20 Asymptotic Expansions of E p ( z )
§8.20(i) Large z
§8.20(ii) Large p
19: 13.8 Asymptotic Approximations for Large Parameters
§13.8 Asymptotic Approximations for Large Parameters
§13.8(i) Large | b | , Fixed a and z
§13.8(ii) Large b and z , Fixed a and b / z
§13.8(iii) Large a
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 | ν | 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 H ν ( x ) and L ν ( x ) can be computed in a stable manner by integrating forwards, that is, from the origin toward infinity. The solution K ν ( x ) needs to be integrated backwards for small x , and either forwards or backwards for large x depending whether or not ν exceeds 1 2 . …