Formula:8081

Digital Library of Mathematical Functions ID 23.22.E1

${\displaystyle{\displaystyle 2\omega_{1}M(1,k^{\prime})=-2i\omega_{3}M(1,k)=\frac{\pi}{3}\sqrt{\frac{c(2+k^{2}{k^{\prime}}^{2})({k^{\prime}}^{2}-k^{2})}{d(1-k^{2}{k^{\prime}}^{2})}},}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\omega_{1}}}$: lattice generators
• ${\displaystyle{\displaystyle M(j,k)}}$: arithmetic-geometric mean
• ${\displaystyle{\displaystyle k}}$: modulus
• ${\displaystyle{\displaystyle k^{\prime}}}$: complementary modulus
 

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