Formula:7372

Digital Library of Mathematical Functions ID 19.30.E3

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

Symbols List

• ${\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: elliptic integral symmetric in only two variables
• ${\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: symmetric elliptic integral of first kind
• ${\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}$: Legendre’s incomplete elliptic integral of the second kind
• ${\displaystyle{\displaystyle\phi}}$: real or complex argument
• ${\displaystyle{\displaystyle k}}$: real or complex modulus
• ${\displaystyle{\displaystyle s}}$: arclength
 

Resources that cite this formula

No records found.