# elementary

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## 1—10 of 92 matching pages

##### 2: Bibliography X
• G. L. Xu and J. K. Li (1994) Variable precision computation of elementary functions. J. Numer. Methods Comput. Appl. 15 (3), pp. 161–171 (Chinese).
• ##### 3: 17.17 Physical Applications
See Kassel (1995). …
##### 4: Karl Dilcher
Dilcher’s research interests include classical analysis, special functions, and elementary, combinatorial, and computational number theory. …
##### 6: 19.36 Methods of Computation
When the differences are moderately small, the iteration is stopped, the elementary symmetric functions of certain differences are calculated, and a polynomial consisting of a fixed number of terms of the sum in (19.19.7) is evaluated. …
19.36.1 $1-\tfrac{1}{10}E_{2}+\tfrac{1}{14}E_{3}+\tfrac{1}{24}E_{2}^{2}-\tfrac{3}{44}E_% {2}E_{3}-\tfrac{5}{208}E_{2}^{3}+\tfrac{3}{104}E_{3}^{2}+\tfrac{1}{16}E_{2}^{2% }E_{3},$
where the elementary symmetric functions $E_{s}$ are defined by (19.19.4). …
19.36.2 $1-\tfrac{3}{14}E_{2}+\tfrac{1}{6}E_{3}+\tfrac{9}{88}E_{2}^{2}-\tfrac{3}{22}E_{% 4}-\tfrac{9}{52}E_{2}E_{3}+\tfrac{3}{26}E_{5}-\tfrac{1}{16}E_{2}^{3}+\tfrac{3}% {40}E_{3}^{2}+\tfrac{3}{20}E_{2}E_{4}+\tfrac{45}{272}E_{2}^{2}E_{3}-\tfrac{9}{% 68}(E_{3}E_{4}+E_{2}E_{5}).$
19.36.4 \begin{aligned} \displaystyle z_{1}&\displaystyle=2.10985\;99098\;8,\\ \displaystyle z_{3}&\displaystyle=2.15673\;49098\;8,\\ \displaystyle Z_{1}&\displaystyle=0.00977\;77253\;5,\end{aligned}\quad\begin{% aligned} \displaystyle z_{2}&\displaystyle=2.12548\;49098\;8,\\ \displaystyle A&\displaystyle=2.13069\;32432\;1,\\ \displaystyle Z_{2}&\displaystyle=0.00244\;44313\;4,\end{aligned}\\ {Z_{3}=-Z_{1}-Z_{2}=-0.01222\;21566\;9,}\\ {E_{2}=\Sci{-1.25480\;14}{-4},\quad E_{3}=\Sci{-2.9212}{-7}.}
##### 7: 4.1 Special Notation
 $k,m,n$ integers. …
It is assumed the user is familiar with the definitions and properties of elementary functions of real arguments $x$. …
##### 8: 14.31 Other Applications
###### §14.31(ii) Conical Functions
These functions are also used in the Mehler–Fock integral transform (§14.20(vi)) for problems in potential and heat theory, and in elementary particle physics (Sneddon (1972, Chapter 7) and Braaksma and Meulenbeld (1967)). …
##### 9: 19.19 Taylor and Related Series
Define the elementary symmetric function $E_{s}(\mathbf{z})$ by
19.19.4 $\prod_{j=1}^{n}(1+tz_{j})=\sum_{s=0}^{n}t^{s}E_{s}(\mathbf{z}),$
19.19.5 $T_{N}(\mathbf{\tfrac{1}{2}},\mathbf{z})=\sum(-1)^{M+N}{\left(\tfrac{1}{2}% \right)_{M}}\frac{E_{1}^{m_{1}}(\mathbf{z})\cdots E_{n}^{m_{n}}(\mathbf{z})}{m% _{1}!\cdots m_{n}!},$
The number of terms in $T_{N}$ can be greatly reduced by using variables $\mathbf{Z}=\boldsymbol{{1}}-(\mathbf{z}/A)$ with $A$ chosen to make $E_{1}(\mathbf{Z})=0$. …
$E_{1}(\mathbf{Z})=0$ , $|Z_{j}|<1$.