Formula:7211

Digital Library of Mathematical Functions ID 19.25.E11

${\displaystyle{\displaystyle E\left(\phi,k\right)=-\tfrac{1}{3}{k^{\prime}}^{2}R_{D}\left(c-k^{2},c,c-1\right)+\sqrt{(c-k^{2})/(c(c-1))},}}$

Constraint(s)

${\displaystyle{\displaystyle\phi\neq\tfrac{1}{2}\pi}}$

Symbols List

• ${\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: elliptic integral symmetric in only two variables
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}$: Legendre’s incomplete elliptic integral of the second kind
• ${\displaystyle{\displaystyle\phi}}$: real or complex argument
• ${\displaystyle{\displaystyle k}}$: real or complex modulus
• ${\displaystyle{\displaystyle k^{\prime}}}$: complementary modulus
 

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