# symmetric case

(0.002 seconds)

## 1—10 of 34 matching pages

##### 1: 28.29 Definitions and Basic Properties
In the symmetric case $Q(z)=Q(-z)$, $w_{\mbox{\tiny I}}(z,\lambda)$ is an even solution and $w_{\mbox{\tiny II}}(z,\lambda)$ is an odd solution; compare §28.2(ii). …
##### 3: 19.20 Special Cases
###### §19.20 Special Cases
The general lemniscatic case is … where $x,y,z$ may be permuted. … The general lemniscatic case is …
##### 4: 19.21 Connection Formulas
19.21.15 $pR_{J}\left(0,y,z,p\right)+qR_{J}\left(0,y,z,q\right)=3R_{F}\left(0,y,z\right),$ $pq=yz$.
##### 6: Bille C. Carlson
Symmetric integrals and their degenerate cases allow greatly shortened integral tables and improved algorithms for numerical computation. …
##### 7: 20.9 Relations to Other Functions
In the case of the symmetric integrals, with the notation of §19.16(i) we have …
##### 8: 19.15 Advantages of Symmetry
Define the elementary symmetric function $E_{s}(\mathbf{z})$ by … 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 $E_{1}(\mathbf{Z})=0$. … Special cases are given in (19.36.1) and (19.36.2).