Theory and Modern Applications
ρ | p | q | ϕ(ϑ) |
---|---|---|---|
1 | \(-(1+m^{2})\) | \(m^{2}\) | sn(ϑ) |
\(1-m^{2}\) | \(2 m^{2}-1\) | \(-m^{2}\) | cn(ϑ) |
\(m^{2}-1\) | \(2-m^{2}\) | -1 | dn(ϑ) |
\(\frac{1}{4}\) | \(\frac{1-2 m^{2}}{2}\) | \(\frac{1}{4}\) | ns(ϑ)±cs(ϑ) or \(\frac{sn(\vartheta)}{1 \pm cn(\vartheta)}\) |
\(\frac{1-m^{2}}{4}\) | \(\frac{1+m^{2}}{2}\) | \(\frac{1-m^{2}}{4}\) | nc(ϑ)±sc(ϑ) or \(\frac{cn(\vartheta)}{1 \pm sn(\vartheta)}\) |
1 | \(2-m^{2}\) | \(1-m^{2}\) | sc(ϑ) |
\(1-m^{2}\) | \(2-m^{2}\) | 1 | cs(ϑ) |