Formula:7206

Digital Library of Mathematical Functions ID 19.25.E6

${\displaystyle{\displaystyle\frac{\partial F\left(\phi,k\right)}{\partial k}=\tfrac{1}{3}kR_{D}\left(c-1,c,c-k^{2}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: elliptic integral symmetric in only two variables
• ${\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}$: Legendre’s incomplete elliptic integral of the first kind
• ${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$: partial derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\partial\NVar{x}}}$: partial differential of $$x$$
• ${\displaystyle{\displaystyle\phi}}$: real or complex argument
• ${\displaystyle{\displaystyle k}}$: real or complex modulus
 

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