Formula:6796

Digital Library of Mathematical Functions ID 19.2.E12

${\displaystyle{\displaystyle\mathrm{el2}\left(x,k_{c},a,b\right)=\int_{0}^{\operatorname{arctan}x}\frac{a+b{\tan^{2}}\theta}{\sqrt{(1+{\tan^{2}}\theta)(1+k_{c}^{2}{\tan^{2}}\theta)}}\mathrm{d}\theta.}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}$:
• ${\displaystyle{\displaystyle\tan\NVar{z}}}$: tangent function
• ${\displaystyle{\displaystyle a}}$: polynomial
• ${\displaystyle{\displaystyle b}}$: real parameter
• ${\displaystyle{\displaystyle k_{c}}}$: real parameter not equal to zero
• ${\displaystyle{\displaystyle x}}$: real or complex variable not equal to zero
 

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