Formula:6825

Digital Library of Mathematical Functions ID 19.4.E9

${\displaystyle{\displaystyle(k{k^{\prime}}^{2}D_{k}^{2}+{k^{\prime}}^{2}D_{k}+k)E\left(\phi,k\right)=\frac{k\sin\phi\cos\phi}{\sqrt{1-k^{2}{\sin^{2}}\phi}}.}}$

Symbols List

• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}$: Legendre’s incomplete elliptic integral of the second kind
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle\phi}}$: real or complex argument
• ${\displaystyle{\displaystyle k}}$: real or complex modulus
• ${\displaystyle{\displaystyle k^{\prime}}}$: complementary modulus
• ${\displaystyle{\displaystyle D_{k}}}$: differential operator
 

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