DLMF:19.4.E8

MaRDI QIDQ6824

• Label: DLMF:19.4.E8

Digital Library of Mathematical Functions ID 19.4.E8

${\displaystyle{\displaystyle(k{k^{\prime}}^{2}D_{k}^{2}+(1-3k^{2})D_{k}-k)F\left(\phi,k\right)=\frac{-k\sin\phi\cos\phi}{(1-k^{2}{\sin^{2}}\phi)^{3/2}},}}$

Symbols List

• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}$: Legendre’s incomplete elliptic integral of the first 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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