# numerical use of

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## 1—10 of 77 matching pages

##### 1: 11.13 Methods of Computation
A comprehensive approach is to integrate the defining inhomogeneous differential equations (11.2.7) and (11.2.9) numerically, using methods described in §3.7. …
##### 2: Publications
• B. V. Saunders and Q. Wang (1999) Using Numerical Grid Generation to Facilitate 3D Visualization of Complicated Mathematical Functions, Technical Report NISTIR 6413 (November 1999), National Institute of Standards and Technology. • ##### 3: 2.11 Remainder Terms; Stokes Phenomenon
###### §2.11(i) NumericalUse of Asymptotic Expansions
The rest of this section is devoted to general methods for increasing this accuracy. …
###### §2.11(vi) Direct Numerical Transformations
However, direct numerical transformations need to be used with care. …For example, extrapolated values may converge to an accurate value on one side of a Stokes line (§2.11(iv)), and converge to a quite inaccurate value on the other.
##### 4: Barry I. Schneider
He has authored or co-authored 140 refereed papers and books and has given numerous invited talks in the US and abroad. …
##### 5: 5.21 Methods of Computation
Another approach is to apply numerical quadrature (§3.5) to the integral (5.9.2), using paths of steepest descent for the contour. …
##### 6: 21.2 Definitions
For numerical purposes we use the scaled Riemann theta function $\hat{\theta}\left(\mathbf{z}\middle|\boldsymbol{{\Omega}}\right)$, defined by (Deconinck et al. (2004)), …
##### 7: Bibliography L
• J. L. López and N. M. Temme (2010a) Asymptotics and numerics of polynomials used in Tricomi and Buchholz expansions of Kummer functions. Numer. Math. 116 (2), pp. 269–289.
• ##### 8: 10.47 Definitions and Basic Properties
###### §10.47(iii) Numerically Satisfactory Pairs of Solutions
For (10.47.1) numerically satisfactory pairs of solutions are given by Table 10.2.1 with the symbols $J$, $Y$, $H$, and $\nu$ replaced by $\mathsf{j}$, $\mathsf{y}$, $\mathsf{h}$, and $n$, respectively. For (10.47.2) numerically satisfactory pairs of solutions are ${\mathsf{i}^{(1)}_{n}}\left(z\right)$ and $\mathsf{k}_{n}\left(z\right)$ in the right half of the $z$-plane, and ${\mathsf{i}^{(1)}_{n}}\left(z\right)$ and $\mathsf{k}_{n}\left(-z\right)$ in the left half of the $z$-plane. …
##### 9: Bibliography G
• A. Gil, J. Segura, and N. M. Temme (2003b) Computing special functions by using quadrature rules. Numer. Algorithms 33 (1-4), pp. 265–275.
• ##### 10: Mathematical Introduction
In referring to the numerical tables and approximations we use notation typified by $x=0(.05)1$, 8D or 8S. …