Theory and Modern Applications
Table 1 Jacobi elliptic functions
Solution | \(\boldsymbol{q_{2}}\) | \(\boldsymbol{q_{4}}\) | F |
|---|---|---|---|
1 | \(-(1+M^{2})\) | \(M^{2}\) | sn |
2 | \(2M^{2}-1\) | \(-M^{2}\) | cn |
3 | \(2-M^{2}\) | −1 | dn |
4 | \(-(1+M^{2})\) | 1 | ns |
5 | \(2M^{2}-1\) | \(1-M^{2}\) | nc |
6 | \(2-M^{2}\) | \(M^{2}-1\) | nd |
7 | \(2-M^{2}\) | \(1-M^{2}\) | sc |
8 | \(2M^{2}-1\) | \(-M^{2}(1-M^{2})\) | sd |
9 | \(2-M^{2}\) | 1 | cs |
10 | \(-(1+M^{2})\) | \(M^{2}\) | cd |
11 | \(2M^{2}-1\) | 1 | ds |
12 | \(-(1+M^{2})\) | 1 | dc |
13 | \(M^{2}/2-1\) | \(M^{4}/4\) | sn/(1 + dn) |
14 | \(M^{2}/2-1\) | \(M^{4}/4\) | \(\mathrm{cn}/(\sqrt{1-M^{2}}+\mathrm{dn})\) |