Table of Integrals, Series, and Products, 8th Edition

Functional relations

8.154

1. 

${\text{sn}}^{2}u=\frac{1-\text{cn}2u}{1+\text{dn}2u}$

  MO 146

2. 

${\text{cn}}^{2}u=\frac{\text{cn}2u+\text{dn}2u}{1+\text{dn}2u}$

  MO 146

3. 

${\text{dn}}^{2}u=\frac{\text{dn}2u+k^2\text{cn}2u+{k^{\prime }}^2}{1+\text{dn}2u}$

  MO 146

4. 

${\text{sn}}^{2}u+{\text{cn}}^{2}u=1$

  SI 16(9)

5. 

${\text{dn}}^{2}u+k^2{\text{sn}}^{2}u=1$

  SI 16(9)

8.155

1. 

$\frac{1-\text{dn}2u}{1+\text{dn}2u}=k^2\frac{{\text{sn}}^{2}u{\text{cn}}^{2}u}{{\text{dn}}^{2}u}$

  MO 146

2. 

$\frac{1}{}$